Skip to main content
SpringerLink
Log in

Condensing operators

  • Published:
Journal of Soviet Mathematics Aims and scope Submit manuscript

Abstract

This paper is devoted to a survey of the current state of the theory of measures of noncompactness and condensing operators.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature cited

  1. L. M. Averina and B. N. Sadovskii, “Local solvability of functional-differential equations of neutral type,” Tr. Mat. Fak. Voronezh. Gos. Univ., No. 3, 1–12 (1971).

    Google Scholar 

  2. R. R. Akhmerov, “Averaging principle for systems of functional-differential equations of neutral type,” in: Materials of the Third All-Union Inter-University Conference on the Theory and Applications of Differential Equations with Deflected Argument [in Russian], Chernovtsy (1972), pp. 14–15.

  3. R. R. Akhmerov, “Averaging principle for functional-differential equations of neutral type,” Ukr. Mat. Zh.,25, No. 5, 579–588 (1973).

    Google Scholar 

  4. R. R. Akhmerov, “Existence of solutions of the Cauchy problem for a class of functional-differential equations of outstripping type,” in: Materials of the Ninth Scientific Conference of the Faculty of Physics-Mathematics and Natural Sciences, 1973 [in Russian], Moscow (1974), pp. 5–7.

  5. R. R. Akhmerov, “Averaging principle on the entire axis for equations of neutral type,” Differents. Uravn.,13, No. 8, 1506 (1977).

    Google Scholar 

  6. R. R. Akhmerov, “Theory of equations of neutral type. Theory of operator equations,” Voronezh (1979), pp. 3–16.

  7. R. R. Akhmerov, V. A. Vyazovikin, and A. E. Rodkina, “Remark on the paper of V. F. Subbotin and V. F. Pulyaev ‘Existence of solutions of systems of differential equations with deflected argument’,” in: Collected Papers of Graduate Students. Mathematical Faculty of Voronezh University [in Russian], Voronezh (1972), pp. 4–8.

  8. R. R. Akhmerov, N. G. Kazakova, and A. V. Pokrovskii, “Principle of the absence of bounded solutions and absolute stability of equations of neutral type,” Serdika. B"lg. Mat. Spisanie,1, 61–69 (1978).

    Google Scholar 

  9. R. R. Akhmerov and M. I. Kamenskii, “N. N. Bogolyubov's second theorem for functional-differential equations of neutral type,” in: Materials of the Third All-Union Inter-University Conference on the Theory and Applications of Differential Equations with Deflected Argument [in Russian], Chernovtsy (1972), pp. 15–17.

  10. R. R. Akhmerov and M. I. Kamenskii, “Averaging principle and stability of periodic solutions of equations of neutral type,” Tr. NII Mat. Voronezh. Gos. Univ., No. 15, 9–13 (1974).

    Google Scholar 

  11. R. R. Akhmerov and M. I. Kamenskii, “N. N. Bogolyubov's second theorem in the averaging principle for functional-differential equations of neutral type,” Differents. Uravn.,10, No. 3, 537–540 (1974).

    Google Scholar 

  12. R. R. Akhmerov and M. I. Kamenskii, “An approach to the study of stability of periodic solutions in the averaging principle for functional-differential equations of neutral type,” Comment. Math. Univ. Carol.,16, No. 2, 293–313 (1975).

    Google Scholar 

  13. R. R. Akhmerov and M. I. Kamenskii, “Stability of an equilibrium state of functional-differential equations with small deflected argument,” Usp. Mat. Nauk,30, No. 2, 205–206 (1975).

    Google Scholar 

  14. R. R. Akhmerov and M. I. Kamenskii, “Stability of solutions of equations of neutral type,” in: Fourth All-Union Conference on the Theory and Applications of Differential Equations with Deflected Argument [in Russian], Naukova Dumka, Kiev (1975), pp. 20–21.

    Google Scholar 

  15. R. R. Akhmerov and M. I. Kamenskii, “Bifurcation in strongly continuous families of operators,” in: Seventh All-Union Topological Conference [in Russian], Minsk (1977), p. 13.

  16. R. R. Akhmerov and M. I. Kamenskii, “Stability in the first approximation to an ensemble of dynamical systems,” in: Proceedings of the Fifth All-Union Conference-Seminar on Control of Large Systems [in Russian], Alma-Ata (1978), pp. 114–115.

  17. R. R. Akhmerov and M. I. Kamenskii, “Equations with small deflected argument,” in: All-Union Conference on Asymptotic Methods in the Theory of Singular Perturbations of Equations [in Russian], Part 2, Alma-Ata (1979), pp. 10–12.

  18. R. R. Akhmerov, M. I. Kamenskii, V. S. Kozyakin, and A. V. Sobolev, “Periodic solution of systems of autonomic functional-differential equations of neutral type with small lag,” Differents. Uravn.,10, No. 11, 1923–1931 (1974).

    Google Scholar 

  19. R. R. Akhmerov and A. E. Rodkina, “Differential inequalities and the structure of an integral whirlpool of systems of functional-differential equations of neutral type,” in: Materials of the Third All-Union Inter-University Conference on the Theory and Applications of Differential Equations with Deflected Argument [in Russian], Chernovtsy (1972), pp. 17–18.

  20. R. R. Akhmerov and A. E. Rodkina, “Differential inequalities and the structure of an integral whirlpool of systems of functional-differential equations of neutral type,” Differents. Uravn.,9, No. 5, 797–806 (1973).

    Google Scholar 

  21. A. L. Badoev and B. N. Sadovskii, “Examples of a condensing operator in the theory of differential equations with deflected argument of neutral type,” Dokl. Akad. Nauk SSSR,186, No. 6, 1239–1242 (1969).

    Google Scholar 

  22. V. A. Bondarenko, “Existence of a universal measure of noncompactness,” in: Problems of Mathematical Analysis of Complex Systems [in Russian], No. 2, Voronezhsk. Gos. Univ., Voronezh (1968), pp. 18–21.

    Google Scholar 

  23. Yu. G. Borisovich, “Topological theory of nonlinear mappings in Banach spaces,” in: Seventh Summer Mathematics School, 1969 [in Russian], Kiev (1970), pp. 274–282.

  24. Yu. G. Borisovich, B. D. Gel'man, A. D. Myshkis, and V. V. Obukhovskii, “Topological methods in the theory of fixed points of multivalued mappings,” Usp. Mat. Nauk,35, No. 1, 59–126 (1980).

    Google Scholar 

  25. Yu. G. Borisovich and L. M., Margulis, “Topological degree of nonlinear noncompact mappings,” Tr. NII Mat. Voronezh. Gos. Univ., No. 5, 19–27 (1972).

    Google Scholar 

  26. Yu. G. Borisovich and Yu. I. Sapronov, “Topological theory of condensing operators,” Dokl. Akad. Nauk SSSR,183, No. 1, 18–20 (1968).

    Google Scholar 

  27. Yu. G. Borisovich and Yu. I. Sapronov, “Topological theory of compactly carried mappings,” Tr.Semin. Funkts. Anal. Voronezh. Gos. Univ., No. 12, 43–68 (1969).

    Google Scholar 

  28. K. Borsuk, Theory of Retracts [Russian translation], Mir, Moscow (1971).

    Google Scholar 

  29. V. G. Brodovskii, “A boundary problem for differential equations with deflected argument,” KazSSR Gylym Akad. Khabarlary, Izv. Akad. Nauk KazSSR, Ser. Fiz. Mat., No. 5, 25–30 (1970).

    Google Scholar 

  30. G. M. Vainikko, “Principle of compact approximation in the theory of approximation methods,” Zh. Vychisl. Mat. Mat. Fiz.,9, No. 4, 739–761 (1969).

    Google Scholar 

  31. G. M. Vainikko, Compact Approximation of Operators and Approximate Solution of Equations [in Russian], Tartus. Gos. Univ., Tartu (1970).

    Google Scholar 

  32. G. M. Vainikko, Analysis of Methods of Discretization [in Russian], Special Course, Tartus. Gos. Univ., Tartu (1976).

    Google Scholar 

  33. G. M. Vainikko and B. N. Sadovskii, “Rotation of condensing vector fields,” in: Problems of Mathematical Analysis of Complex Systems [in Russian], No. 2, Voronezhsk. Gos. Univ., Voronezh (1968), pp. 84–88.

    Google Scholar 

  34. Yu. N. Vladimirskii, “Compact approximation in Banach spaces,” Sib. Mat. Zh.,15, No. 1, 200–204 (1974).

    Google Scholar 

  35. E. A. Gango, “Theorems on fixed points of multivalued mappings,” Uch. Zap. Leningr. Gos. Pedagog. Inst. im.A.I. Gertsena,464, 137–146 (1970).

    Google Scholar 

  36. V. M. Gershtein, “Dissipative differential equations in a Banach space,” Funkts. Anal. Prilozhen.,4, No. 3, 99–100 (1970).

    Google Scholar 

  37. V. M. Gershtein, “Dissipative flows,” Tr. Mat. Fak. Voronezh. Gos. Univ., No. 1, 26–34 (1970).

    Google Scholar 

  38. Yu. E. Gliklikh, “Translation operator along trajectories of functional-differential equations on smooth manifolds,” Tr. NII Mat. Voronezh. Gos. Univ., No. 17, 18–24 (1975).

    Google Scholar 

  39. Yu. E. Gliklikh, “Pseudointegral curves of functional-differential equations on Riemannian manifolds,” in: Methods of Solution of Operator Equations [in Russian], Voronezh (1978), pp. 28–33.

  40. L. S. Gol'denshtein, I. Ts. Gokhberg, and A. S. Markus, “Properties of bounded linear operators studied with the help of the q-norm,” Uch. Zap. Kishinevsk. Gos. Univ., No. 29, 29–36 (1957).

    Google Scholar 

  41. L. S. Gol'denshtein and A. S. Markus, “Measure of noncompactness of bounded sets and linear operators,” in: Studies in Algebra and Mathematical Analysis [in Russian], Kartya Moldovenyaske, Kishinev (1965), pp. 45–54.

    Google Scholar 

  42. Ya. I. Gol'tser and A. M. Zverkin, “Existence and uniqueness of solutions of differential equations with delay in a Banach space,” Différents. Uravn.,12, No. 8, 1404–1409 (1976).

    Google Scholar 

  43. G. M. Goncharov, “Generalization of a theorem of Leray-Schauder,” Tr. Tsentr. Zonal'n. Ob"edin. Mat. Kafedr. Kalinin. Gos. Pedagog. Inst., No. 1, 80–85 (1970).

    Google Scholar 

  44. G. M. Goncharov, “Existence theorems for solutions for a class of nonlinear operator equations,” Mat. Zametki,7, No. 2, 229–237 (1970).

    Google Scholar 

  45. I. Ts. Gokhberg and M. G. Krein, “Basic situation of defect numbers, root numbers, and indices of linear operators,” Usp. Mat. Nauk,12, No. 2, 43–118 (1957).

    Google Scholar 

  46. N. M. Gulevich and A. I. Povolotskii, “Fixed points of operators in Hilbert space,” in: Theory of Functions and Functional Analysis [in Russian], Leningrad (1975), pp. 42–45.

  47. Yu. A. Dyadchenko, “Local solvability of operator equations,” in: Qualitative and Approximate Methods of Investigation of Operator Equations [in Russian], No. 3, Yaroslavl' (1978), pp. 48–60.

    Google Scholar 

  48. Yu. A. Dyadchenko, “Solvability of a nonlinear operator equation of Volterra type,” in: Theory of Operator Equations [in Russian], Voronezh (1979), pp. 22–33.

  49. P. P. Zabreiko, “Cauchy problem for ordinary differential equations in Banach spaces,” God. Vissh. Tekh. Uchebn. Zaved. Prilozhna Mat.,11, No. 1, 53–60 [1975 (1976–1977)].

    Google Scholar 

  50. P. P. Zabreiko, M. A. Krasnosel'skii, and V. V. Strygin, “Invariance of rotation principles,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 5, 51–57 (1972).

    Google Scholar 

  51. P. P. Zabreiko and I. B. Ledovskaya, “Existence theorems for equations in a Banach space and the averaging principle,” in: Problems of the Mathematical Analysis of Complex Systems [in Russian], No. 3, Voronezh. Gos. Univ. (1968), pp. 122–136.

  52. P. P. Zabreiko and Yu. I. Fetisov, “Application of the Bogolyubov-Krylov averaging method to hyperbolic equations,” Vestn. Yaroslav. Gos. Univ., No. 7, 150–155 (1974).

    Google Scholar 

  53. Ya. A. Izrailevich and V. V. Obukhovskii, “Topological characteristics of equivariant multivalued mappings,” Tr. Mat. F-ta, Voronezh. Gos. Univ., No. 10, 52–61 (1973).

    Google Scholar 

  54. A. A. Kalmykov, “Fixed points of condensing operators, expanding a cone,” Uch. Zap. Perm. Gos. Univ., No. 309, 29–32 (1974).

    Google Scholar 

  55. A. A. Kalmykov, (k, χ)-Boundedness Conditions for Integral Operators in Spaces of Functions Continuous and Bounded on an Infinite Interval [in Russian], Perm. Gos. Univ., Perm' (1977).

    Google Scholar 

  56. A. A. Kalmykov, Projective Measures of Noncompactness and Projective Condensing Operators [in Russian], Perm. Gos. Univ., Perm' (1977).

    Google Scholar 

  57. G. A. Kamenskii and A. D. Myshkis, “Boundary problems for a nonlinear differential equation with deflected argument of neutral type,” Differents. Uravn.,8, No. 12, 2171–2179 (1972).

    Google Scholar 

  58. M. I. Kamenskii, “Theory of the degree of a map,” Tr. Mat. Fak. Voronezh. Gos. Univ., No. 4, 54–60 (1971).

    Google Scholar 

  59. M. I. Kamenskii, “Calculation of the rotation of a condensing vector field,” Sb. Voronezh. Gos. Univ.,2, 32–36 (1972).

    Google Scholar 

  60. M. I. Kamenskii, “Two theorems on the existence of a periodic solution of a functional-differential equation of neutral type,” in: Materials of the Third All-Union Inter-University Conference on the Theory and Applications of Differential Equations with Deflected Argument [in Russian], Chernovtsy (1972), pp. 100–102.

  61. M. I. Kamenskii, “Peano's theorem in infinite-dimensional spaces,” Mat. Zametki,11, No. 5, 569–576 (1972).

    Google Scholar 

  62. M. I. Kamenskii, “Theory of perturbations of bounded operators in a Banach space,” in: Collection of Graduate Students' Papers [in Russian], No. 2, Voronezh. Gos. Univ. (1974), pp. 18–23.

  63. M. I. Kamenskii, “Calculation of the index of an isolated solution of the Cauchy problem for functional-differential equations of neutral type,” in: Functional Analysis and Its Applications [in Russian], No. 1, Voronezh (1973), pp. 6–13.

    Google Scholar 

  64. M. I. Kamenskii, “Andronov-Witt's theorem for functional-differential equations of neutral type,” Tr. NII Mat. Voronezh. Gos. Univ., No. 12, 31–36 (1974).

    Google Scholar 

  65. M. I. Kamenskii, “Translation operator along trajectories of equations of neutral type,” in: Collection of Graduate Students' Papers on the Theory of Functions and Differential Equations [in Russian], Voronezh (1974), pp. 19–22.

  66. M. I. Kamenskii, “Theory of periodic solutions for functional-differential equations of neutral type,” Tr. NII Mat. Voronezhsk. Gos. Univ., No. 15, 32–36 (1974).

    Google Scholar 

  67. M. I. Kamenskii, “Stability of linear systems of equations of neutral type,” in: Fourth All-Union Conference on the Theory and Applications of Differential Equations with Deflected Argument [in Russian], Naukova Dumka, Kiev (1975), pp. 110–111.

    Google Scholar 

  68. M. I. Kamenskii, “Noncompactness measures and the theory of perturbations of linear operators,” Uch. Zap. Tartus. Gos. Univ., No. 430, 112–122 (1977).

    Google Scholar 

  69. M. I. Kamenskii, “Translation operator along trajectories of equations of neutral type depending on a parameter,” Uch. Zap. Tartus. Gos. Univ., No. 448/21, 107–117 (1978).

    Google Scholar 

  70. M. I. Kamenskii and R. R. Akhmerov, “N. N. Bogolyubov's theorems in the averaging principle,” in: All-Union Conference on the Qualitative Theory of Differential Equations and Methods of Instruction in the Theory of Differential Equations in Pedagogical Institutes [in Russian], Ryazan' (1976), pp. 157–158.

  71. V. S. Kozyakin, “Condensing and compressing operators,” Tr. Mat. Fak. Voronezh. Gos. Univ., No. 1, 60–70 (1970).

    Google Scholar 

  72. M. A. Krasnosel'skii, Topological Methods in the Theory of Nonlinear Integral Equations [in Russian], Gostekhizdat, Moscow (1956).

    Google Scholar 

  73. M. A. Krasnosel'skii, “Some new fixed point principles,” Dokl. Akad. Nauk SSSR,208, No. 6, 1280–1281 (1973).

    Google Scholar 

  74. M. A. Krasnosel'skii and P. P. Zabreiko, Geometric Methods of Nonlinear Analysis [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  75. M. A. Krasnosel'skii and S. G. Krein, “Theory of ordinary differential equations in a Banach space,” Tr. Semin. Funkts. Anal. Voronezhsk. Gos. Univ., No. 2, 3–23 (1956).

    Google Scholar 

  76. K. Kuratowski, Topology, Vol. 1, Academic Press (1966).

  77. V. G. Kurbatov, “Spectral radii and Fredholm radii of certain linear operators in the space of functions continuous and bounded on the axis,” in: Collection of Graduate Students' Papers [in Russian], No. 2, Voronezh. Gos. Univ. (1972), pp. 47–51.

  78. E. A. Lifshits and B. N. Sadovskii, “Fixed point theorem for generalized condensing maps,” Dokl. Akad. Nauk SSSR,183, No. 2, 278–279 (1968).

    Google Scholar 

  79. G. B. Lyal'kina, “Generalization of Schaefer's principle to condensing operators,” Uch. Zap. Perm. Gos. Univ., No. 309, 13–19 (1974).

    Google Scholar 

  80. G. B. Lyal'kina, “Derivatives and derivatives with respect to a cone of a (k,ψ)-bounded operator,” Uch. Zap. Perm. Gos. Univ., No. 291, 14–16 (1975).

    Google Scholar 

  81. G. B. Lyal'kina, “Repelling points of a condensing operator in a Banach space with cone,” Uch. Zap. Perm. Gos. Univ., No. 291, 22–24 (1975).

    Google Scholar 

  82. G. B. Lyal'kina, “Fixed points of positive condensing operators strongly asymptotic to linear ones with respect to a cone,” Uch. Zap. Perm. Gos. Univ., No. 291, 25–30 (1975).

    Google Scholar 

  83. G. B. Lyal'kina, “Galerkin's method of convergence with perturbations for equations with condensing operators,” Uch. Zap. Perm. Gos. Univ., No. 291, 31–33 (1975).

    Google Scholar 

  84. G. B. Lyal'kina, “Conditions for a Uryson operator to be χ-condensing in spaces C and Lp,” in: Functional-Differential Equations and Boundary Problems of Mathematical Physics [in Russian], Perm' (1978), pp. 166–168.

  85. G. B. Lyal'kina and A. A. Kalmykov, “An attracting point of a condensing operator in a semiordered Banach space,” Uch. Zap. Perm. Gos. Univ., No. 291, 17–21 (1975).

    Google Scholar 

  86. V. M. Millionshchikov, “Differential equations in locally convex spaces,” Mat. Sb.,57, No. 4, 385–406 (1962).

    Google Scholar 

  87. I. V. Misyurkeev, “Existence of fixed points of condensing operators strongly asymptotically linear with respect to a cone,” Uch. Zap. Perm. Gos. Univ., No. 309, 20–25 (1974).

    Google Scholar 

  88. I. V. Misyurkeev and G. B. Lyal'kina, “Study of a class of nonlinear integral equations by topological methods,” Uch. Zap. Perm. Gos. Univ., No. 271, 20–25 (1973).

    Google Scholar 

  89. I. Muntyan, “Fixed point theorem in locally convex spaces,” Rev. Roum. Math. Pures Appl.,19, No. 9, 1105–1109 (1974).

    Google Scholar 

  90. A. M. Mukhsinov, “Differential inclusions in Banach spaces,” Dokl. Akad. Nauk SSSR,217, No. 4, 759–761 (1974).

    Google Scholar 

  91. V. R. Nosov, “Massera-Halanyi theorem for linear systems of neutral type,” in: Materials of the Ninth Scientific Conference of the Faculty of Physical-Mathematical and Natural Sciences of P. Lumumba University of Friendly Peoples [in Russian], Moscow (1974), pp. 42–43.

  92. V. V. Obukhovskii, “Fixed point principles for multivalued condensing operators,” Tr. Mat. Fak. Voronezh. Gos. Univ., No. 4, 70–79 (1971).

    Google Scholar 

  93. V. V. Obukhovskii, “Rotation of condensing multivalued vector fields,” in: Abstracts of the Sixth All-Union Topology Conference [in Russian], Metsniereba, Tbilisi (1972), pp. 93–94.

    Google Scholar 

  94. V. V. Obukhovskii, “The degree for a class of noncompact multivalued mappings,” in: School on the Theory of Operators in Function Spaces [in Russian], Minsk (1978), pp. 102–103.

  95. V. V. Obukhovskii and E. V. Gorokhov, “Definition of the rotation of a class of compactly carried multivalued vector fields,” Tr. Mat. Fak. Voronezh. Gos. Univ., No. 12, 45–54 (1974).

    Google Scholar 

  96. R. Palais, Seminar on the Atiyah-Singer Index Theorem [Russian translation], Mir, Moscow (1970).

    Google Scholar 

  97. V. V. Petrishin, “Extension of Sheffer's theorem to many-valued contraction operators,” Dopovidi Akad. Nauk Ukr. RSR, A, No. 10, 889–891, 956 (1973).

    Google Scholar 

  98. A. S. Potapov, “Calculation of the index of an isolated singular point of a condensing vector field Φ=I-A with sufficiently smooth operator A,” in: Collection of Students' Scientific Papers [in Russian], Voronezh. Gos. Univ. (1972), pp. 89–92.

  99. A. S. Potapov, “Estimates of the Fredholm radius of a linear operator,” Tr. NII Mat. Voronezh. Gos. Univ., No. 5, 108–113 (1972).

    Google Scholar 

  100. A. S. Potapov, “Measure of noncompactness of certain sets,” in: Functional Analysis and Its Applications [in Russian], No. 1, Voronezh (1973), pp. 23–27.

    Google Scholar 

  101. A. S. Potapov, “Rotation of multivalued vector fields,” in: Collection of Graduate Students' Papers [in Russian], No. 2, Voronezh. Gos. Univ. (1974), pp. 41–44.

  102. A. S. Potapov, “Theory of rotation of limit compact vector fields,” Comment. Math. Univ. Carol.,15, No. 4, 693–716 (1974).

    Google Scholar 

  103. A. S. Potapov, “K-operators and measures of noncompactness,” Tr. Mat. Fak. Voronezh. Gos. Univ., No. 16, 34–40 (1975).

    Google Scholar 

  104. A. S. Potapov, T. Ya. Potapova, and V. A. Filin, “Fixed points and eigenvectors of positive condensing operators,” Comment. Math. Univ. Carol.,18, No. 2, 219–230 (1977).

    Google Scholar 

  105. A. S. Potapov and B. N. Sadovskii, “Difference of classes Kn,” Tr. Mat. Fak. Voronezh. Gos. Univ., No. 16, 40–44 (1975).

    Google Scholar 

  106. A. S. Potapov and B. N. Sadovskii, “Rotation of a class of noncompact vector fields,” in: Seventh All-Union Topology Conference [in Russian], Minsk (1977), p. 155.

  107. A. E. Rodkina, “A version of the topological connectivity principle,” Usp. Mat. Nauk,30, No. 2, 225–226 (1975).

    Google Scholar 

  108. A. E. Rodkina and B. N. Sadovskii, “Krasnosel'skii-Perova connectivity principle,” Tr. Mat. Fak. Voronezhsk. Gos. Univ., No. 4, 89–103 (1971).

    Google Scholar 

  109. A. E. Rodkina and B. N. Sadovskii, “Differentiation of the translation operator along trajectories of an equation of neutral type,” Tr. Mat. Fak. Voronezh. Gos. Univ., No. 12, 31–37 (1974).

    Google Scholar 

  110. B. N. Sadovskii, “A fixed point principle,” Funkts. Anal. Prilozhen.,1, No. 2, 74–76 (1967).

    Google Scholar 

  111. B. N. Sadovskii, “Measures of noncompactness and condensing operators,” in; Problems of Mathematical Analysis of Complex Systems [in Russian], No. 2, Voronezhsk. Gos. Univ., Voronezh (1968), pp. 89–119.

    Google Scholar 

  112. B. N. Sadovskii, “Local solvability of ordinary differential equations in a Banach space,” in; Problems of Mathematical Analysis of Complex Systems [in Russian], No. 3, Voronezh (1968), pp. 232–243.

    Google Scholar 

  113. B. N. Sadovskii, “Condensing operators and measures of noncompactness,” Tr. Mat. Fak. Voronezh. Gos. Univ., No. 1, 112–124 (1970).

    Google Scholar 

  114. B. N. Sadovskii, “Differential equations with uniformly continuous right side,” Tr. NII Mat. Voronezh. Gos. Univ., No. 1, 128–136 (1970).

    Google Scholar 

  115. B. N. Sadovskii, “Application of topological methods to the theory of periodic solutions of nonlinear differential-operator equations of neutral type,” Dokl. Akad. Nauk SSSR,200, No. 5, 1037–1040 (1971).

    Google Scholar 

  116. B. N. Sadovskii, “Limit compact and condensing operators,” Usp. Mat. Nauk,27, No. 1, 81–146 (1972).

    Google Scholar 

  117. B. N. Sadovskii, “Periodic solution of functional-differential equations of neutral type,” in: Materials of the Third All-Union Inter-University Conference on the Theory and Applications of Differential Equations with Deflected Argument [in Russian], Chernovtsy (1972), pp. 176–177.

  118. B. N. Sadovskii, “Theory of rotation of limit compact vector fields and its applications,” in: Sixth All-Union Topology Conference [in Russian], Metsniereba, Tbilisi (1972), p. 105.

    Google Scholar 

  119. B. N. Sadovskii, “Equations of neutral type and condensing operators,” in: Fourth Ail-Union Conference on the Theory and Applications of Differential Equations with Deflected Argument [in Russian], Naukova Dumka, Kiev (1975), pp. 210–211.

    Google Scholar 

  120. B. N. Sadovskii, “Three new results in the theory of measures of noncompactness and condensing operators,” in: School on Theory of Operators in Function Spaces [in Russian], Minsk (1978), pp. 128–130.

  121. B. N. Sadovskii, “Condensing operators and differential equations,” Preprint IM Sib. Otd. Akad. Nauk SSSR (School on Theory of Operators in Function Spaces), Novosibirsk (1979).

    Google Scholar 

  122. Yu. I. Sapronov, “Algebraic theory of the index,” Tr. Semin. Funkts. Anal. Voronezhsk. Gos. Univ., No. 12, 143–154 (1969).

    Google Scholar 

  123. Yu. I. Sapronov, “Rotation of vector fields with condensing operators,” in: Collection of Students' Papers [in Russian], Voronezh. Gos. Univ., No. 3, 15–20 (1970).

  124. Yu. I. Sapronov, “Homotopy classification of condensing maps,” Tr. Mat. Fak. Voronezh. Gos. Univ. No. 6, 78–80 (1972).

    Google Scholar 

  125. A. A. Sedaev, “Structure of certain linear operators,” in; Mathematical Studies [in Russian], Vol. 5, No. 1, Kishinev (1970), pp. 166–175.

    Google Scholar 

  126. A. A. Tolstonogov, “Classical solution of differential inclusions in Banach spaces with nonconvex right side,” in: Nonlinear Oscillations and the Theory of Control [in Russian], No. 2, Izhevsk (1978), pp. 16–23.

    Google Scholar 

  127. A. A. Tolstonogov, “Differential inclusions in Banach spaces and continuous selectors,” Dokl. Akad. Nauk SSSR,244, No. 5, 1088–1092 (1979).

    Google Scholar 

  128. A. A. Tolstonogov, “Properties of inclusions in a Banach space,” Dokl. Akad. Nauk SSSR,248, No. 1, 42–46 (1979).

    Google Scholar 

  129. V. A. Filin, “Solvability of operator equations with condensing operators,” Dokl. Akad. Fankhoi RSS Tochikiston. Dokl. Akad. Nauk TadzhSSR,17, No. 10, 12–15 (1974).

    Google Scholar 

  130. V. A. Filin, “Existence of an eigenvalue of a quasi-positive operator,” in: Theory of Functions and Functional Analysis [in Russian], Dushanbe (1979), pp. 92–96.

  131. V. A. Filin, “Positive solutions of a nonlinear integral equation,” in: Theory of Functions and Functional Analysis [in Russian], Dushanbe (1979), pp. 97–101.

  132. Khatch Olia, “Existence of solution of system of differential equations in locally convex space,” Mat. Vesn.12, No. 1, 63–70 (1975).

    Google Scholar 

  133. A. V. Kholodkov, “Solvability of a differential-operator equation of neutral type with a Volterra type operator,” in: Questions of Computational and Applied Mathematics [in Russian], No. 25, Tashkent (1974), pp. 3–9.

    Google Scholar 

  134. A. V. Kholodkov, “Averaging of differential-operator equations of neutral type,” in: Questions of Computational and Applied Mathematics [in Russian], No. 28, Tashkent (1974), pp. 69–79.

    Google Scholar 

  135. M. Alić, “Measures of noncompactness and seminorms,” Glas. Mat.,9, No. 2, 267–271 (1974).

    Google Scholar 

  136. H. Amann, “On the number of solutions of nonlinear equations in ordered Banach spaces,” J. Funct. Anal.,11, No. 3, 346–384 (1972).

    Google Scholar 

  137. H. Amann, “Fixed points of asymptotically linear maps in ordered Banach spaces,” J. Funct. Anal.,14, No. 2, 162–171 (1973).

    Google Scholar 

  138. H. Amann, “Nonlinear operators in ordered Banach spaces and some applications to nonlinear boundaryvalue problems,” Lect. Notes Math.,543, 1–55 (1976).

    Google Scholar 

  139. A. Ambrosetti, “Un theorema di esistenza per le equazioni differenziali negli spazi di Banach,” Rend. Semin. Mat. Univ. Padova,39, 349–361 [1967 (1968)].

    Google Scholar 

  140. A. Ambrosetti, “Proprietà spettrali di certi operatori linear! non compatti,” Rend. Sem. Mat. Univ. Padova,42, 188–200 (1969).

    Google Scholar 

  141. C. J. Amick, “Some remarks on Rellich's theorem and the Poincaré inequality,” J. London Math. Soc.,18, No. 1, 81–93 (1978).

    Google Scholar 

  142. J. Appell, Approximierbare Operatoren in normierten und lokalkonvexen Räumen, Inauguraldiss., Freien Univ. Berlin, Berlin (1978).

    Google Scholar 

  143. Z. Artstein, “On continuous dependence of fixed points of condensing maps,” Preprint (1974).

  144. Z. Artstein, “Continuous dependence of solutions of operator equations. I,” Trans. Am. Math. Soc.,231, No. 1, 143–166 (1977).

    Google Scholar 

  145. T. D. Benavides, “An existence theorem for implicit differential equations in a Banach space,” Ann. Mat. Pura Appl.,118, 119–130 (1978).

    Google Scholar 

  146. S. Bernfeld and V. Lakshmikantham, “Monotone methods for nonlinear boundary value problems in Banach spaces,” Nonlinear Analysis: Theory, Methods, and Appl.,3, No. 3, 303–316 (1979).

    Google Scholar 

  147. S. Bernfeld, V. Lakshmikantham, and Y. M. Reddy, “Fixed points of operators with PPE dependence in Banach spaces,” Appl. Anal.,6, No. 4, 271–280 (1977).

    Google Scholar 

  148. R. Bittner and T. Pruszko, “On the application of operational calculus to the problem of the existence and uniqueness of solutions of nonlinear differential equations,” Demonstr. Math.,10, Nos. 3–4, 705–730 (1977).

    Google Scholar 

  149. G. Bossan, “Some remarks on a measure of noncompactness in probabilistic metric spaces,” Bull. Math. Soc. Sci. Math. RSR,20, Nos. 1–2, 41–44 (1976(1977)].

    Google Scholar 

  150. Ju. G. Borisovič and Ju. E. Gliklih, “Fixed points of mappings of Banach manifolds and some applicaations,” Nonlinear Anal.: Theory, Meth., Appl.,4, No. 1, 165–192 (1980).

    Google Scholar 

  151. F. E. Browder, “Recent results in nonlinear functional analysis and applications to partial differential equations,” in: Actes Congr. Int. Matematiciens, 1970, Vol. 2, Paris (1971), pp. 821–829.

    Google Scholar 

  152. F. E. Browder, Nonlinear Operators and Nonlinear Equations of Evolution, Am. Math. Soc., Providence (1976).

    Google Scholar 

  153. F. E. Browder and R. D. Nussbaum, “The topological degree for noncompact, nonlinear mapping in Banach spaces,” Bull. Am. Math. Soc.,74, No. 4, 671–676 (1968).

    Google Scholar 

  154. H. Buley, “Fixed point theorems of Rothe-type for Frum-Ketkov and 1-set contractions,” Comment. Math. Univ. Carol.,19, No. 2, 213–225 (1978).

    Google Scholar 

  155. B. Calvert, “Fixed points for U + C where U is Lipschitz and C is compact,” Yokohama Math. J.,25, No. 1, 1–4 (1977).

    Google Scholar 

  156. A. Cellina, “On the existence of solutions of ordinary differential equations in Banach spaces,” Funkc. Ekvacig.,14, No. 2, 129–136 (1971).

    Google Scholar 

  157. J. Chandra, V. Lakshmikantham, and A. R. Mitchell, “Existence of solutions of boundary value problems for nonlinear second-order systems in a Banach space,” Nonlinear Anal.: Theory, Meth. Appl.,2, No. 2, 157–168 (1978).

    Google Scholar 

  158. H. Chatterjee, “Remark on some theorems of K. Iseki,” Indian J. Pure Appl. Math.,10, No. 2, 158–160 (1979).

    Google Scholar 

  159. Martin F. Cheng, “On continuity of fixed points of collectively condensing maps,” Proc. Am. Math. Soc.,63, No. 1, 74–76 (1977).

    Google Scholar 

  160. Martin F. Cheng, “On certain condensing operators and the behavior of their fixed points with respect to parameters,” J. Math. Anal. Appl.,64, No. 3, 505–517 (1978).

    Google Scholar 

  161. Shui-Nee Chow and J. K. Hale, “Strongly limit-compact maps,” Funkc. Ekvacig,17, No. 1, 31–38 (1974).

    Google Scholar 

  162. Shui-Nee Chow and J. K. Hale, “Periodic solutions of autonomous equations,” J. Math. Anal. Appl.,66, No. 3, 495–506 (1978).

    Google Scholar 

  163. Gh. Constantin, “Some spectral properties for the locally α-contraction operators,” Boll. Unione Mat. Ital.,6, No. 3, 323–330 (1972).

    Google Scholar 

  164. G. Conti and P. Nistri, “A fixed point theorem for noncompact acyclic-valued maps,” Rend. Accad. Sci. Fis. Mat. Soc. Naz. Sci. Lett. Arti Napoli,42, 510–517 [1975(1976)].

    Google Scholar 

  165. M. Cousland, “An A-proper map with prescribed topological degree,” Proc. Am. Math. Soc.,58, 179–184 (1976).

    Google Scholar 

  166. E. Cramer, V. Lakshmikantham, and A. R. Mitchell, “On the existence of weak solutions of differential equations in nonreflexive Banach spaces,” Nonlinear Anal.: Theory, Meth. Appl.,2, No. 2, 169–177 (1978).

    Google Scholar 

  167. S. J. Daher, “On a fixed point principle of Sadovskii,” Nonlinear Anal.: Theory, Meth. Appl.,2, No. 5, 643–645 (1978).

    Google Scholar 

  168. S. J. Daher, “Fixed point theorems for nonlinear operators with a sequential condition,” Nonlinear Anal.: Theory, Meth. Appl.,3, No. 1, 59–63 (1979).

    Google Scholar 

  169. J. Daneš, “Generalized concentrative mappings and fixed points,” Summer School on Fixed Points, Krkonoše, Czechoslovakia, Aug. 31–Sept. 6, 1969

  170. J. Daneš, “Generalized concentrative mappings and their fixed points,” Comment. Math. Univ. Carol.11, No. 1, 115–136 (1970).

    Google Scholar 

  171. J. Daneš, “Fixed point theorems, Nemyckii and Uryson operators and continuity of nonlinear mappings,” Comment. Math. Univ. Carol,11, No. 3, 481–500 (1970).

    Google Scholar 

  172. J. Daneš, “Some fixed point theorems in metric and Banach spaces,” Comment. Math. Univ. Carol,12, No. 1, 37–51 (1971).

    Google Scholar 

  173. J. Daneš, “Surjectivity and fixed point theorems (Prelim, commun.),” Comment. Math. Univ. Carol,13, No. 1, 181–184 (1972).

    Google Scholar 

  174. J. Daneš, “On densifying and related mappings and their application in nonlinear functional analysis,” Schriftenr. Zentralinst. Mach. Meth., No. 20, 15–56 (1974).

    Google Scholar 

  175. J. Daneš, “On Istratescu's measure of noncompactness,” Bull. Math. Soc. Sci. Math. RSR,16, No. 4, 403–406 [1972(1974)].

    Google Scholar 

  176. J. Daneš, “Two fixed point theorems in topological and metric spaces,” Bull. Austral. Math. Soc.,14, No. 2, 259–266 (1976).

    Google Scholar 

  177. G. Darbo, “Punti uniti in transformazioni a codominio non compatto,” Rend. Seminar. Mat. Univ. Padova, Parte 1,24, 84–92 (1955).

    Google Scholar 

  178. F. S. de Blasi, “The measure of the weak noncompactness of the unit sphere in a Banach space is either zero or one,” Ist. Mat. Ulisse Dini, Univ. Studi Firenze, Preprint No. 7, 1974–1975.

  179. F. S. de Blasi, “A local approach to the differentiability of multifunctions,” Ist. Mat. Ulisse Dini, Univ. Studi Firenze, Preprint No. 13, 1974–1975.

  180. F. S. de Blasi, “Existence and stability of solutions for autonomous multivalued differential equations in Banach space,” Ist. Mat. Ulisse Dini, Univ. Studi Firenze, Preprint No. 14, 1974–1975.

  181. F. S. de Blasi, “Compactness gauges and fixed points,” Atti Accad. Naz. Lincei, Cl. Sci. Fis., Mat. Natur. Rend.,57, Nos. 3–4, 170–176 [1974(1975)].

    Google Scholar 

  182. F. S. de Blasi, “Existence and stability of solutions for autonomous multivalued differential equations in Banach space,” Atti Accad. Naz. Lincei. Cl. Sci. Fis., Mat. Natur. Rend.,60, No. 6, 767–774 (1976).

    Google Scholar 

  183. F. S. de Blasi, “On the differentiability of multifunctions,” Pacific J. Math.,66, No. 1, 67–81 (1976).

    Google Scholar 

  184. F. S. de Blasi, “On a property of the unit sphere in a Banach space,” Bull. Math. Soc. Sci. Math. RSR,21, Nos. 3–4, 259–262 (1977).

    Google Scholar 

  185. S. Deb and S. P. Singh, “Fixed point theorems in topological vector spaces,” Ann. Soc. Sci. Bruxelles, Ser. I,88, No. 3, 273–280 (1974).

    Google Scholar 

  186. K. Deimling, “On existence and uniqueness for Cauchy's problem in infinite dimensional Banach spaces,” Differ. Equat. 15. Colloq. Math. Soc. János Bolyai, Keszthely, 1974, Amsterdam e.a. (1977), pp. 131–142.

  187. K. Deimling, “Periodic solutions of differential equations in Banach spaces,” Manuscr. Math.,24, No. 1, 31–44 (1978).

    Google Scholar 

  188. J. Dugundji, “An extension of Tietze's theorem,” Pacific J. Math.,1, No. 2, 353–387 (1951).

    Google Scholar 

  189. M. Edelstein and R. C. O'Brien, “Nonexpansive mappings, asymptotic regularity and successive approximations,” J. London Math. Soc.,17, No. 3, 547–554 (1978).

    Google Scholar 

  190. D. E. Edmunds, A. J. B. Potter, and C. A. Stuart, “Noncompact positive operators,” Proc. R. Philos. Soc., Ser. A,328, 67–81 (1972).

    Google Scholar 

  191. D. E. Edmunds and J. R. L. Webb, “Nonlinear operator equations in Hilbert spaces,” J. Math. Anal. Appl.,34, No. 3, 471–478 (1971).

    Google Scholar 

  192. D. E. Edmunds and J. R. L. Webb, “Some generalizations of the Borsuk-Ulam theorem,” Math. Proc. Cambridge Philos. Soc.,82, No. 1, 119–125 (1977).

    Google Scholar 

  193. J. Eisenfeld and V. Lakshmikantham, “Fixed point theorems through abstract cones,” J. Math. Anal. Appl.,52, No. 1, 25–35 (1975).

    Google Scholar 

  194. J. Eisenfeld and V. Lakshmikantham, “On a measure of nonconvexity and applications,” Yokohama Math. J.,24, Nos. 1–2, 133–140 (1976).

    Google Scholar 

  195. J. Eisenfeld and V. Lakshmikantham, “On the existence of solutions of differential equations in a Banach space,” Rev. Roum. Math. Pures Appl.,22, No. 9, 1215–1221 (1977).

    Google Scholar 

  196. J. Eisenfeld and V. Lakshmikantham, “Remarks on nonlinear contraction and comparison principle in abstract cones,” J. Math. Anal. Appl.,61, No. 1, 116–121 (1977).

    Google Scholar 

  197. J. Eisenfeld, V. Lakshmikantham, and S. R. Bernfeld, “On the construction of a norm associated with the measure of noncompactness,” Nonlinear Anal.: Theory, Meth. Appl.,1, No. 1, 49–54 (1976).

    Google Scholar 

  198. C. Fenske, “Analytische Theorie des Abbildungsgrades für Abbildungen in Banachräumen,” Math. Nachr.,48, Nos. 1–6, 279–290 (1971).

    Google Scholar 

  199. C. Fenske, “Leray-Schauder Theorie für eine Klasse differenzierbarer Abbildungen Banachräumen,” Ber. Ges. Math. Datenverarb., No. 48 (1971).

  200. P. M. Fitzpatrick, “A generalized degree for uniform limits of A-proper mappings,” J. Math. Anal. Appl.,35, No. 3, 536–552 (1971).

    Google Scholar 

  201. P. M. Fitzpatrick, “On the structure of the set of equations involving A-proper mappings,” Trans. Am. Math. Soc.,189, 107–131 (1974).

    Google Scholar 

  202. P. M. Fitzpatrick, “Existence results for equations involving noncompact perturbations of Fredholm mappings with applications to differential equations,” J. Math. Anal. Appl.,66, No. 1, 151–177 (1978).

    Google Scholar 

  203. P. M. Fitzpatrick and W. V. Petryshyn, “Fixed point theorems for multivalued noncompact acyclic mappings,” Pacific J. Math.,54, No. 2, 17–23 (1974).

    Google Scholar 

  204. P. M. Fitzpatrick and W. V. Petryshyn, “Fixed point theorems and the fixed point index for multivalued mappings in cones,” J. London Math. Soc.,12, No. 1, 75–85 (1975).

    Google Scholar 

  205. P. M. Fitzpatrick and W. V. Petryshyn, “Positive eigenvalues for nonlinear multivalued noncompact operators with applications to differential operators,” J. Different. Equat.,22, No. 2, 428–441 (1976).

    Google Scholar 

  206. P. M. Fitzpatrick and W. V. Petryshyn, “On the nonlinear eigenvalue problem T (u)=λC (u), involving noncompact abstract and differential operators,” Boll. Unione Mat. Ital.,B15, No. 1, 80–107 (1978).

    Google Scholar 

  207. G. Fournier and H.-O. Peitgen, “Leray endomorphisms and cone maps,” Ann. Scu. Norm. Super. Pisa. Cl. Sci., No. 1, 149–179 (1978).

    Google Scholar 

  208. B. Fuchssteiner, “Iterations and fixed points,” Pacific J. Math.,68, No. 1, 73–80 (1977).

    Google Scholar 

  209. M. Furi and M. Martelli, “Lefschetz type theorem for the minimal displacement of points under maps defined on a class of ANR's,” Boll. Unione Mat. Ital.,10, No. 1, 174–181 (1974).

    Google Scholar 

  210. M. Furi and M. Martelli, “A characterization of compact filter basis in complete metric spaces,” Rend. Ist. Mat. Univ. Trieste,2, No. 2, 109–113 (1970).

    Google Scholar 

  211. M. Furi and M. Martelli, “On the minimal displacement of points underα-Lipschitz maps in normed spaces,” Boll. Unione Mat. Ital.,9, No. 3, 791–799 (1974).

    Google Scholar 

  212. M. Furi and M. Martelli, “Onα-Lipschitz retractions of the unit closed ball onto its boundary,” Atti Accad. Naz. Lincei. Cl. Sci. Fis., Mat. Natur. Rend.,57, Nos. 1–2, 61–65 [1974(1975)].

    Google Scholar 

  213. M. Furi, M. Martelli, and A. Vignoli, “Contributions to the spectral theory for nonlinear operators on Banach spaces,” 1st. Mat., Univ. dell'Aquila, Preprint No. 5 (1977).

  214. M. Furi and A. Vignoli, “A fixed point theorem in complete metric spaces,” Boll. Unione Mat. Ital.,2, Nos. 4–5, 505–509 (1969).

    Google Scholar 

  215. M. Furi and A. Vignoli, “Fixed points for densifying mappings,” Atti Accad. Naz. Lincei Cl. Sci. Fis., Mat. Natur. Rend.,47, No. 6, 465–467 [1969(1979)].

    Google Scholar 

  216. M. Furi and A. Vignoli, “On a property of the unit sphere in a linear normed space,” Bull. Acad. Sci. Ser. Math., Astron. Phys.,18, No. 6, 333–334 (1970).

    Google Scholar 

  217. M. Furi and A. Vignoli, “Onα-nonexpansive mappings and fixed points,” Atti. Accad. Naz. Lincei. Cl. Sci. Fis. Mat. Natur. Rend.,48, No. 2, 195–198 (1970).

    Google Scholar 

  218. M. Furi and A. Vignoli, “On surjectivity for nonlinear maps in Banach spaces,” Ann. Mat. Pura Appl.,112, 205–216 (1977).

    Google Scholar 

  219. R. E. Gaines and J. L. Mawhin, “Coincidence degree and nonlinear differential equations,” Lect. Notes Math.,568 (1977).

  220. J. A. Gatica, “Fixed point theorems for k-set-contractions and pseudocontractive mappings,” J. Math. Anal. Appl.,46, No. 3, 555–564 (1974).

    Google Scholar 

  221. J. A. Gatica and W. A. Kirk, “Fixed point theorems for Lipschitzian pseudo-contractive mappings,” Proc. Am. Math. Soc.,36, No. 1, 111–115 (1972).

    Google Scholar 

  222. J. A. Gatica and W. A. Kirk, “A fixed point theorem for k-set-contractions defined in a cone,” Pacific J. Math.,53, No. 1, 131–136 (1974).

    Google Scholar 

  223. K. Georg, “On surjectivity of quasibounded nonlinearα-Lipschitz maps,” Boll. Unione Mat. Ital.,13A, No. 1, 117–122 (1976).

    Google Scholar 

  224. O. Hadžić, “Existence of the solution of the equation x=G(x, S(x)) in locally convex spaces,” Math. Balkan,3, 118–123 (1973).

    Google Scholar 

  225. O. Hadzic, “Existence theorems for the system x=H(x, y), y=K(x, y) in locally convex spaces,” Publs. Inst. Math.,16, 65–73 (1973).

    Google Scholar 

  226. O. Hadžić, “Impicit differential equation in locally convex spaces,” Publs. Inst. Math.,19, 67–72 (1975).

    Google Scholar 

  227. O. Hadžić, Osnovij Teoriji Nepokretne Tačke, Novi Sad (1978).

  228. O. Hadžić, “A fixed point theorem for mappings with aψ-densifying iteration in locally convex spaces,” Mat. Vestn.,2, No. 2, 105–109 (1978).

    Google Scholar 

  229. O. Hadžić and D. Paunic, “Theorems on the fixed point for some classes of mappings in locally convex spaces,” Zb. Rad. Prir. Mat. Fak. Gos. Univ. Novom Sadu,6, 25–31 (1976).

    Google Scholar 

  230. S. Hahn, “Gebietsinvarianzsatz und Eigenwertaussagen für konzentrierende Abbildungen,” Comment. Math. Univ. Carol.,18, No. 4, 697–713 (1977).

    Google Scholar 

  231. S. Hahn, “A remark on a fixed point theorem for condensing set-valued mappings,” Techn. Univ. Dresden, Preprint No. 07-5, 1977.

  232. S. Hahn, “Ein elementarer Zugang zur Leray-Schauder-Theorie,” Techn. Univ. Dresden, Preprint No. 07-10, 1977.

  233. S. Hahn, “Eine Bemerkung zur Theorie verdichtender Abbildungen,” Wiss. Z. Techn. Univ. Dresden,27, No. 2, 337–340 (1978).

    Google Scholar 

  234. S. Hahn, “Ein elementarer Zugang zur Leray-Schauder-Theorie,” Comment. Math. Univ. Carol.,19, No. 1, 71–87 (1978).

    Google Scholar 

  235. S. Hahn, “Eigenwertaussagen für kompakte kondensierende mengenwertige Abbildungen in topologischen Vektorräumen,” Comment. Math. Univ. Carol.,20, No. 1, 123–141 (1979).

    Google Scholar 

  236. J. K. Hale, “A class of neutral equations with the fixed point property,” Proc. Nat. Acad. Sci. U.S.A.,67, No. 1, 136–137 (1970).

    Google Scholar 

  237. J. K. Hale, “Oscillations in neutral functional equations,” in: Nonlinear Mech. C.I.M.I. June, 1972, Ediz. Cremonese, Rome (1973), pp. 97–111.

  238. J. K. Hale, “α-contractions and differential equations,” in: Actes Conf. Internat. Equa-Diff73, Hermann, Paris (1973), pp. 15–41.

    Google Scholar 

  239. J. K. Hale, “Smoothing properties of neutral equations,” An. Acad. Brasil Cienc.,45, No. 1, 71–73 (1973).

    Google Scholar 

  240. J. K. Hale, “Continuous dependence of fixed points of condensing maps,” J. Math. Anal. Appl.,46, No. 2, 388–394 (1974).

    Google Scholar 

  241. J. K. Hale, “Functional differential equations with infinite delays,” J. Math. Anal. Appl.,48, No. 1, 276–283 (1974).

    Google Scholar 

  242. J. K. Hale, “Discrete dissipative processes,” Lect. Notes Math.,564, 207–224 (1976).

    Google Scholar 

  243. J. K. Hale, Theory of Functional Differential Equations, Appl. Math. Sci., Vol. 3 (1977).

  244. J. K. Hale and J. Kato, “Phase space for retarded equations with infinite delay,” Funkc. Ekvacioj,21, No. 1, 11–41 (1978).

    Google Scholar 

  245. M. Hegedüs, “An extension of Krasnoselskii's fixed-point theorem for multivalued mappings,” Dep. Math. K. Marx Univ. Econ. Budapest (Publ.), No. 3 (1976).

  246. G. Hetzer, “Some applications of the coincidence degree for set-contractions to functional differential equations of neutral type,” Comment. Math. Univ. Carol.,16, No. 1, 121–138 (1975).

    Google Scholar 

  247. G. Hetzer, “Some remarks on Φ+-operators and on the coincidence degree for a Fredholm equation with noncompact nonlinear perturbations,” Ann. Soc. Sci. Bruxelles, Ser. 1,89, No. 4, 497–508 (1975).

    Google Scholar 

  248. G. Hetzer, J. Reinermann, and V. Stallbohm, “Fixpunktsätze von Browder und Krasnoselski für lokalkonvexe Hausdorff-Räume,” Math. Nachr.,57, Nos. 1–6, 227–235 (1973).

    Google Scholar 

  249. G. Hetzer and V. Stallbohm, “Coincidence degree and Rabinowitz's bifurcation theorem,” Publs. Inst. Math.,20, 117–129 (1976).

    Google Scholar 

  250. G. Hetzer and V. Stallbohm, “Eine Existenzaussage für asymptotische linear Störungen eines Fredholmoperatoren Index 0,” Manuscr. Math.,21, No. 1, 81–100 (1977).

    Google Scholar 

  251. C. J. Himmelberg, J. R. Porter, and F. S. van Vleck, “Fixed point theorems for condensing multifunctions,” Proc. Am. Math. Soc.,23, No. 3, 635–641 (1969).

    Google Scholar 

  252. C. J. Himmelberg and F. S. van Vleck, “Fixed points of semicondensing multifunctions,” Boll. Unione Mat. Ital.,5, No. 2, 187–194 (1972).

    Google Scholar 

  253. K. Iseki, “A generalization of Petryshyn-Riggio-Singh's theorem,” Math. Semin. Notes. Kobe Univ.,2, No. 2, var. pag., 1–3 (1974).

    Google Scholar 

  254. K. Iseki, “Fixed point theorems for densifying mappings,” Nanta Math.,9, No. 1, 50–53 (1976).

    Google Scholar 

  255. A. Istratescu and V. Istratescu, “A generalization of collectively compact sets of operators. I,” Rev. Roum. Math. Pures Appl.,17, No. 1, 33–37 (1972).

    Google Scholar 

  256. A. Istratescu and V. Istratescu, “On the existence of a solution of f(x)=kx for a continuous not necessarily linear operator,” Proc. Am. Math. Soc.,48, No. 1, 197–198 (1975).

    Google Scholar 

  257. I. Istratescu, “On some classes of contractions,” Atti. Accad. Naz. Lincei. Cl. Sci. Fis., Mat. Natur. Rend.,50, No. 6, 679–681 (1971).

    Google Scholar 

  258. I. Istratescu, “Some spectral properties for the I-contraction operators,” Math. Balkan., No. 4, 267–269 (1974).

    Google Scholar 

  259. V. Istratescu, “Capitole de analiza neliniara,” Gar. Mat. (RSR),A77, No. 10, 372–377 (1972).

    Google Scholar 

  260. V. Istratescu, “On a measure of noncompactness,” Bull. Math. Soc. Sci. Math. RSR,16, No. 2, 195–197 [1972(1973)].

    Google Scholar 

  261. V. Istratescu, Introducere in Teoria Punctelor Fixe, Acad. RSR, Bucuresti (1974).

    Google Scholar 

  262. V. Istratescu, “On a class of operators and ergodic theory. I,” Rev. Roum. Math. Pure Appl.,19, No. 4, 411–420 (1974).

    Google Scholar 

  263. V. Istratescu and A. Istratescu, “On the theory of fixed points for some classes of mappings. III,” Atti Accad. Naz. Lincei. Cl. Sci. Fis., Mat. Natur. Rend.,49, Nos. 1–2, 43–46 (1970).

    Google Scholar 

  264. V. Istratescu and A. Istratescu, “On the theory of fixed points for some classes of mappings,” Atti Accad. Naz. Lincei. Cl. Sci. Fis., Mat. Natur. Rend.,51, Nos. 3–4, 162–167 (1971).

    Google Scholar 

  265. V. Istratescu and A. Istratescu, “On the theory of fixed points for some classes of mappings. II,” Rev. Roum. Math. Pures Appl.,16, No. 7, 1073–1075 (1971).

    Google Scholar 

  266. V. Istratescu and A. Istratescu, “On the theory of fixed points for some classes of mappings. I,” Bull. Math. Soc. Sci. Math. RSR,14, No. 4, 420–426 [1970(1972)].

    Google Scholar 

  267. V. Istratescu and A. Istratescu, “On the theory of fixed points for some classes of mappings,” Atti Accad. Naz. Lincei. Cl. Sci. Fis., Mat. Natur. Rend.,52, No. 6, 871–874 (1972).

    Google Scholar 

  268. V. Istratescu and A. Istratescu, “On some results on locally powerα-set contractions. III,” Atti Accad. Naz. Lincei. Cl. Sci. Fis., Mat. Natur. Rend.,56, No. 2, 197–200 (1974).

    Google Scholar 

  269. S. Itoh and W. Takahashi, “Single-valued mappings, multivalued mappings and fixed-point theorems,” J. Math. Anal. Appl.,59, No. 3, 514–521 (1977).

    Google Scholar 

  270. A. F. Izé and J. G. dos Reis, “Contributions to stability of neutral functional differential equations,” J. Different. Equat.,29, No. 1, 58–65 (1978).

    Google Scholar 

  271. R. Janicka, “An existence theorem for an integrodifferential equation of neutral type,” Ann. UMCS,A28, No. 3, 28–29 (1974).

    Google Scholar 

  272. G. S. Jones, “Asymptotic fixed point heory,” Ann. Math. Stud., No. 69, 177–184 (1972).

    Google Scholar 

  273. G. S. Jones, “A functional approach to fixed point analysis of noncompact operators,” Math. Syst. Theory,6, No. 4, 375–382 (1973).

    Google Scholar 

  274. R. K. Juberg, “Measure of noncompactness and interpolation of compactness for a class of integral transformations,” Duke Math. J.,41, No. 3, 511–525 (1974).

    Google Scholar 

  275. R. K. Juberg, “The measure of noncompactness in Lp for a class of integral operators,” Indiana Univ. Math. J.,23, No. 10, 925–936 (1974).

    Google Scholar 

  276. G. Kayser, “Ein Fixpunktsatz für konzentrierende Abbildungen in lokalkonvexen Räumen,” Wiss. Z. Techn. Univ. Dresden,23, No. 1, 145–151 (1974).

    Google Scholar 

  277. G. Kayser, “A fixed point theorem for noncompact setvalued mappings,” Abh. Akad. Wiss. DDR, No. 3, 407–411 (1977).

    Google Scholar 

  278. W. A. Kirk, “A remark on condensing mappings,” J. Math. Anal. Appl.,51, No. 3, 629–632 (1975).

    Google Scholar 

  279. M. Kisieliwicz, “Fixed point theorem for multivalued noncompact mappings,” Zesz. Nauk. WSI Zielonej Gorze, No. 31, 5–7 (1975).

    Google Scholar 

  280. C. Kuratowski, “Sur les espaces complets,” Fund. Math.,15, 301–309 (1930).

    Google Scholar 

  281. C. Kuratowski, Topology, Vol. 1, Academic Press, New York-Warszawa, PWN (1966).

    Google Scholar 

  282. A. Lebow and M. Schechter, “Semigroups of operators and measures of noncompactness,” J. Funct. Anal.,7, No. 1, 1–26 (1971).

    Google Scholar 

  283. S. Leela and V. Moaurdo, “Existence of solutions in a closed set for delay differential equations in Banach spaces,” Nonlinear Anal.: Theory. Math. Appl.,2, No. 1, 47–58 (1978).

    Google Scholar 

  284. R. Leggett, “Remarks on set-contractions and condensing maps,” Math. Z.,132, No. 4, 361–366 (1973).

    Google Scholar 

  285. R. Leggett, “A note on ‘locally’α-contracting linear operators,” Bull. Unione Mat. Ital.,12, Nos. 1–2, 124–126 (1975).

    Google Scholar 

  286. G. Mancini, “Rami di soluzioni positive per operatori non compatti,” Boll. Unione Mat. Ital.,B14, No. 1, 42–58 (1977).

    Google Scholar 

  287. M. Martelli, “A lemma on maps of a compact topological space and an application to fixed point theory,” Ist. Mat. Ulisse Dini, Univ. Studi Firenze, Preprint, 1970.

  288. M. Martelli and A. Vignoli, “Eigen-vectors and surjectivity forα-Lipschitz mappings in Banach spaces,” Ann. Mat. Pura Appl.,94, 1–9 (1972).

    Google Scholar 

  289. M. Martelli and A. Vignoli, “Some surjectivity results for noncompact multivalued maps,” Rend. Acad. Sci. Fis. Mat. Soc. Naz. Sci. Lett. Arti Napoli,41, 57–66 (1974).

    Google Scholar 

  290. M. Martelli and A. Vignoli, “A generalized Leray-Schauder condition,” Atti Accad. Naz. Lincei. Cl. Sci. Fis., Mat. Natur. Rend.,57, No. 5, 374–379 [1974(1975)].

    Google Scholar 

  291. S. Massa and D. Roux, “Applicazioni densificanti e teoremi di punto unito,” Boll. Unione Mat. Ital.,4, No. 6, 835–840 (1971).

    Google Scholar 

  292. I. Massabo, “On the construction of fixed-points for a class of nonlinear mappings,” Boll. Unione Mat. Ital.,10, No. 2, 512–528 (1974).

    Google Scholar 

  293. I. Massabo and P. Nistri, “A topological degree for multivalued A-proper maps in Banach spaces,” Boll. Unione Mat. Ital.,B13, No. 3, 672–685 (1976).

    Google Scholar 

  294. I. Massabo and C. Stuart, “Positive eigenvectors of k-set contractions,” Nonlinear Anal.: Theory, Meth. Appl.,3, No. 1, 35–44 (1979).

    Google Scholar 

  295. P. S. Milojević, “Some generalizations of the first Fredholm theorem to multivalued condensing and A-proper mappings,” Boll. Unione Mat. Ital.,B13, No. 3, 619–633 (1976).

    Google Scholar 

  296. P. S. Milojević, “Some generalizations of the first Fredholm theorem to multivalued A-proper mappings with applications to nonlinear elliptic equations,” J. Math. Anal. Appl.,65, No. 2, 468–502 (1978).

    Google Scholar 

  297. P. S. Milojević, “Fixed point theorem for multivalued approximable mappings,” Proc. Am. Math. Soc.,73, No. 1, 65–72 (1979).

    Google Scholar 

  298. P. S. Milojević and W. V. Petryshyn, “Continuation theorems and the approximation-solvability of equations involving multivalued A-proper mappings,” J. Math. Anal. Appl.,60, No. 3, 658–692 (1977).

    Google Scholar 

  299. P. S. Milojević and W. V. Petryshyn, “Continuation and surjectivity theorems for uniform limits of A-proper mappings with applications,” J. Math. Anal. Appl.,62, No. 2, 368–400 (1978).

    Google Scholar 

  300. H. Mönch and G. -F. von Harten, “The product formula for the topological degree of strictγ-contractions,” Manuscr. Math.,23, No. 2, 113–123 (1978).

    Google Scholar 

  301. M. Montagnana and A. Vignoli, “On quasiconvex mappings and fixed point theorems,” Boll. Unione Mat. Ital.,4, No. 6, 870–878 (1971).

    Google Scholar 

  302. R. H. Moore and M. Z. Nashed, “Local and asymptotic approximations of nonlinear operators by (k1,..., kn)-homogeneous operators,” Trans. Am. Math. Soc.,118, Apr., 293–305 (1973).

    Google Scholar 

  303. R. D. Nussbaum, “The fixed point index and fixed point theorems for k-set-contractions,” Ph. D. Dissertation, Univ. of Chicago (1969).

  304. R. D. Nussbaum, “The fixed point index and asymptotic fixed point theorems for k-set-contractions,” Bull. Am. Math. Soc.,75, No. 3, 490–495 (1969).

    Google Scholar 

  305. R. D. Nussbaum, “The radius of the essential spectrum,” Duke Math. J.,37, No. 3, 473–478 (1970).

    Google Scholar 

  306. R. D. Nussbaum, “Asymptotic fixed point theorems for local condensing maps,” Math. Ann.,191, No. 3, 181–195 (1971).

    Google Scholar 

  307. R. D. Nussbaum, “Estimates for the number of solutions of operator equations,” Appl. Anal.,1, No. 2, 183–200 (1971).

    Google Scholar 

  308. R. D. Nussbaum, “Some fixed point theorems,” Bull. Am. Math. Soc.,77, No. 3, 360–365 (1971).

    Google Scholar 

  309. R. D. Nussbaum, “The fixed point index for local condensing maps,” Ann. Mat. Pura Appl.,89, 217–258 (1971).

    Google Scholar 

  310. R. D. Nussbaum, “Degree theory for local condensing maps,” J. Math. Anal. Appl.,37, No. 3, 741–766 (1972).

    Google Scholar 

  311. R. D. Nussbaum, “Existence and uniqueness theorems for some functional differential equations of neutral type,” J. Different. Equat.,11, No. 3, 607–623 (1972).

    Google Scholar 

  312. R. D. Nussbaum, “Some asymptotic fixed point theorems,” Trans. Am. Math. Soc.,171, Sept., 349–375 (1972).

    Google Scholar 

  313. R. D. Nussbaum, “A generalization of the Ascoli theorem and an application to functional differential equations,” J. Math. Anal. Appl.,35, No. 3, 600–610 (1971).

    Google Scholar 

  314. R. D. Nussbaum, “Periodic solutions of autonomous functional differential equations,” Bull. Am. Math. Soc.,79, No. 4, 811–814 (1973).

    Google Scholar 

  315. R. D. Nussbaum, “Periodic solutions of some nonlinear autonomous functional differential equations, II,” J. Different. Equat.,14, No. 2, 360–394 (1973).

    Google Scholar 

  316. R. D. Nussbaum, “On the uniqueness of the topological degree for k-set-contractions,” Math. Z.,137, No. 1, 1–6 (1974).

    Google Scholar 

  317. R. D. Nussbaum, “Periodic solutions of some nonlinear autonomous functional differential equations,” Ann. Mat. Pura Appl.,101, 263–306 (1974).

    Google Scholar 

  318. R. D. Nussbaum, “Generalizing the fixed point index,” Math. Ann.,228, No. 3, 259–278 (1977).

    Google Scholar 

  319. T. O'Neil and J. W. Thomas, “On the equivalence of multiplicity and the generalized topological degree,” Trans. Am. Math. Soc.,167, May, 333–345 (1972).

    Google Scholar 

  320. E. de Pascale and R. Guzzardi, “On boundary conditions and fixed points forα-non expansive multivalued mappings,” Atti Accad. Naz. Lincei. Cl. Sci. Fis., Mat. Natur. Rend.,58, No. 3, 300–305(1975).

    Google Scholar 

  321. E. de Pascale and R. Guzzardi, “On the boundary values dependence for the topological degree of multivalued noncompact maps,” Boll. Unione Mat. Ital.,13A, No. 1, 110–116 (1976).

    Google Scholar 

  322. J. Jejsachowicz and A. Vignoli, “On differentiability and surjectivity ofα-Lipschitz mappings,” Ann. Mat. Pura Appl.,101, 49–63 (1974).

    Google Scholar 

  323. W. V. Petryshyn, “Structure of fixed-points sets of k-set-contractions,” Arch. Ration. Mech. Anal.,40, No. 4, 312–328 (1971).

    Google Scholar 

  324. W. V. Petryshyn, “A new fixed point theorem and its application,” Bull. Am. Math. Soc.,78, No. 2, 225–229 (1972).

    Google Scholar 

  325. W. V. Petryshyn, “Note on the structure of fixed point sets of 1-set-contractions,” Proc. Am. Math. Soc.,31, No. 1, 189–194 (1972).

    Google Scholar 

  326. W. V. Petryshyn, “Remarks on condensing and k-set-contractive mappings,” J. Math. Anal. Appl.,39, No. 3, 717–741 (1972).

    Google Scholar 

  327. W. V. Petryshyn, “Fixed point theorems for various classes of 1-set-contractive and 1-ball-contractive mappings in Banach spaces,” Trans. Am. Math. Soc.,182, Aug., 323–352 (1973).

    Google Scholar 

  328. W. V. Petryshyn, “Fredholm alternative for nonlinear k-ball-contractive mappings with applications,” J. Different. Equat.,17, No. 1, 82–95 (1975).

    Google Scholar 

  329. W. V. Petryshyn, “Note on the solvability of equations involving unbounded linear and quasibounded non-linear operators,” J. Math. Anal. Appl.,56, No. 3, 495–501 (1976).

    Google Scholar 

  330. W. V. Petryshyn, “Bifurcation and asymptotic bifurcation for equations involving A-proper mappings with applications to differential equations,” J. Different. Equat.,28, No. 1, 124–154 (1978).

    Google Scholar 

  331. W. V. Petryshyn and P. M. Fitzpatrick, “Degree theory for noncompact multivalued vector fields,” Bull. Am. Math. Soc.,79, No. 3, 609–613 (1973).

    Google Scholar 

  332. W. V. Petryshyn and P. M. Fitzpatrick, “On 1-set and 1-ball contractions with application to perturbation problems for nonlinear bijective maps and linear Fredholm maps,” Bull. Unione Mat. Ital.,7, No. 1, 102–124 (1973).

    Google Scholar 

  333. W. V. Petryshyn and P. M. Fitzpatrick, “A degree theory, fixed point theorems, and mappings theorems for multivalued noncompact mappings,” Trans. Amer. Math. Soc.,194, 1–25 (1974).

    Google Scholar 

  334. W. V. Petryshyn and P. M. Fitzpatrick, “Fixed-point theorems for multivalued noncompaet inward maps,” J. Math. Anal. Appl.,46, No. 3, 756–767 (1974).

    Google Scholar 

  335. W. V. Petryshyn and T. E. Williamson, Jr., “Strong and weak convergence of the sequence of successive approximations for quasi-nonexpansive mappings,” J. Math. Anal. Appl.,43, No. 2, 459–497 (1973).

    Google Scholar 

  336. G. Pianigiani, “Existence of solutions for ordinary differential equations in Banach spaces,” Bull. Acad. Pol. Sci., Ser. Sci. Math., Astron., Phys.,23, No. 8, 853–857 (1975).

    Google Scholar 

  337. A. J. B. Potter, “Non-linear A-proper mappings of the analytic type,” Can. J. Math.,25, No. 3, 468–474 (1973).

    Google Scholar 

  338. A. J. B. Potter, “A fixed point theorem for positive k-set contractions,” Proc. Edinburgh Math. Soc.,19, No. 1, 93–102 (1974).

    Google Scholar 

  339. B. K. Ray, “On common fixed points. III,” Indian J. Pure Appl. Math.,6, No. 11, 1256–1260 (1975).

    Google Scholar 

  340. B. K. Ray and H. Chatterjee, “On some results on fixed points in metric and Banach spaces,” Indian J. Pure Appl. Math.,8, No. 8, 955–960 (1977).

    Google Scholar 

  341. B. K. Ray and H. Chatterjee, “Some results on fixed points in metric and Banach spaces,” Bull. Acad. Pol. Sci. Ser. Sci. Math., Astron. Phys.,25, No. 12, 1243–1247 (1977).

    Google Scholar 

  342. B. K. Ray and S. P. Singh, “Fixed point theorems in Banach spaces,” Indian J. Pure Appl. Math.,9, No. 3, 216–221 (1978).

    Google Scholar 

  343. S. Reich, “A fixed point theorem,” Atti Accad. Naz. Lincei. Cl. Sci. Fis., Mat. Natur. Rend.,51, Nos. 1–2, 26–28 (1971).

    Google Scholar 

  344. S. Reich, “Characteristic vectors of nonlinear operators,” Atti Accad. Naz. Lincei. Cl. Sci. Fis., Mat. Natur. Rend.,50, No. 6, 682–685 (1971).

    Google Scholar 

  345. S. Reich, “Fixed points in locally convex spaces,” Math. Z.,125, No. 1, 17–31 (1972).

    Google Scholar 

  346. S. Reich, “Fixed points of condensing functions,” J. Math. Anal. Appl.,41, No. 2, 460–467 (1973).

    Google Scholar 

  347. S. Reich, “A remark on set-valued mappings that satisfy the Leray-Schauder condition,” Atti Accad. Naz. Lincei. Cl. Sci. Fis., Mat. Natur. Rend.,61, Nos. 3–4, 193–194 [1976(1977)].

    Google Scholar 

  348. S. Reich, “A minimal displacement problem,” Comment. Math. Univ. St. Pauli,26, No. 2, 131–135 (1978).

    Google Scholar 

  349. S. Reich, “Constructing zeros of accretive operators,” Appl. Anal.,8, No. 4, 349–352 (1979).

    Google Scholar 

  350. J. Reinermann, “Fortsetzung stetiger Abbildungen in Banach-Räumen und Anwendungen in der Fixpunkttheorie,” Ber. Ges. Math. Datenverarb., No. 57, 135–145 (1972).

    Google Scholar 

  351. J. Reinermann, “Neue Existenz-und Konvergenzsätze in der Fixpunkttheorie nichtlinearer Operatoren,” J. Approxim. Theory,8, No. 4, 387–399 (1973).

    Google Scholar 

  352. J. Reinermann and V. Stallbohm, “Fixed point theorems for compact and nonexpansive mappings on starshaped domains (Preliminary communication),” Comment. Math. Univ. Carol.,15, No. 4, 775–779 (1974).

    Google Scholar 

  353. J. Reinermann and V. Stallbohm, “Fixed point theorems for compact and nonexpansive mappings on starshaped domains,” Math. Balkan., No. 4, 511–516 (1974).

    Google Scholar 

  354. T. Riedrich, “Nonlinear operator equations in topological vector spaces,” Techn. Univ. Dresden, Preprint No. 07-04, 1975.

  355. T. Riedrich, Vorlesungen über nichtlineare Operatorengleichungen, Leipzig (1976).

  356. A. M. Rossi and P. Sambucetti, “Sulla compattezza negli spazi Lp,” Pubbl. Ist. Mat. Univ. Genova, No. 258 (1978).

  357. E. H. Rothe, “Expository introduction to some aspects of degree theory,” in: Nonlinear Funct. Anal. Different. Equations, New York-Basel (1976), pp. 291–317.

  358. B. Rzepecki, “On the method of Euler polygons for the differential equation in a locally convex space,” Bull. Acad. Pol. Sci. Ser. Sci. Math., Astron. Phys.,23, No. 4, 411–414 (1975).

    Google Scholar 

  359. B. Rzepecki, “Measure of noncompactness and Krasnoselskii's fixed point theorem,” Bull. Acad. Pol. Sci. Ser. Sci. Math., Astron. Phys.,24, No. 10, 861–866 (1976).

    Google Scholar 

  360. B. Rzepecki, “A functional differential equation in Banach space. I,” Funct. Approxim.,5, 13–23 (1977).

    Google Scholar 

  361. R. Schöneberg, “On the structure of fixed point sets of pseudocontractive mappings,” Comment. Math. Univ. Carol.,17, No. 4, 771–777 (1976).

    Google Scholar 

  362. R. Schöneberg, “On the structure of fixed point sets of pseudocontractive mappings, II,” Comment. Math. Univ. Carol.,18, No. 2, 299–310 (1977).

    Google Scholar 

  363. R. Schöneberg, “Leray-Schauder principles for condensing multivalued mappings in topological linear spaces,” Proc. Am. Math. Soc.,72, No. 2, 268–270 (1978).

    Google Scholar 

  364. R. Schöneberg, “A note on connection properties of fixed point sets of nonexpansive mappings,” Math. Nachr.,83, 247–253 (1978).

    Google Scholar 

  365. V. M. Sehgal, “A fixed point theorem for a family of nonexpansive mappings,” Bull. Austral. Math. Soc.,15, No. 1, 111–116 (1976).

    Google Scholar 

  366. G. R. Sell, “A characterization of smoothα-Lipschitz mappings on a Hilbert space,” Atti Accad. Naz. Lincei. Cl. Sci. Fis., Mat. Natur. Rend.,52, No. 5, 668–674 (1972).

    Google Scholar 

  367. K. L. Singh, “Fixed point theorems for densifying maps. I,” Math. Stud.,40, 283–288 [1972(1974)].

    Google Scholar 

  368. K. L. Singh, “Some applications of Darbo's theorem,” Atti Accad. Naz. Lincei. Cl. Sci. Fis., Mat. Natur. Rend.,58, No. 6, 880–886 (1975).

    Google Scholar 

  369. K. L. Singh, “Eignevalues of densifying mappings,” Atti Accad. Naz. Lincei. Cl. Sci. Fis., Mat. Natur. Rend.,59, Nos. 1–2, 34–39 [1975(1976)].

    Google Scholar 

  370. K. L. Singh, “Some applications of Darbo's theorem,” Bull. Math. Soc. Sci. Math. RSR,19, Nos. 1–2, 181–187 [1975(1976)].

    Google Scholar 

  371. K. L. Singh, “Some applications of Kuratowski's measure of noncompactness,” Atti Accad. Naz. Lincei. Cl. Sci. Fis., Mat. Natur. Rend.,60, No. 4, 422–432 (1976).

    Google Scholar 

  372. K. L. Singh, “Two theorems characterizing increasing k-set contraction mappings,” Atti Accad. Naz. Lincei. Cl. Sci. Fis., Mat. Natur. Rend.,59, No. 6, 749–757 [1975(1976)].

    Google Scholar 

  373. K. L. Singh, “A note on the spectra of uniformly increasing densifying mappings,” Bull. Acad. Pol. Sci. Ser. Sci. Math., Astron. Phys.,24, No. 11, 969–972 [1976(1977)].

    Google Scholar 

  374. K. L. Singh, “Convergence of sequence of iterates of generalized contractions,” Atti Accad. Naz. Lincei. Cl. Sci. Fis., Nat. Natur. Rend.,62, No. 2, 154–159 (1977).

    Google Scholar 

  375. K. L. Singh, “Solvability of linear and nonlinear operator equations involving densifying mappings,” Bull. Math. Soc. Sci. Math. RSR,20, Nos. 3–4, 403–414 [1976(1977)].

    Google Scholar 

  376. K. L. Singh, “A fixed point theorem for multivalued densifying mappings,” Mathematica (RSR),20, No. 1, 71–75 (1978).

    Google Scholar 

  377. K. L. Singh, “Construction of fixed points for densifying mappings,” Riv. Mat. Univ. Parma,4, 55–62 (1978).

    Google Scholar 

  378. S. P. Singh, “Fixed point theorems for a sum of nonlinear operators,” Atti Accad. Naz. Lincei, Cl. Sci. Fis., Mat. Natur. Rend.,54, No. 4, 558–561 (1973).

    Google Scholar 

  379. S. P. Singh, “On a theorem of Reinermann,” Atti Accad. Naz. Lincei. Cl. Sci. Fis., Mat. Natur. Rend.,54, No. 1, 46–48 (1973).

    Google Scholar 

  380. S. P. Singh, “On the convergence of iterates,” Atti Accad. Naz. Lincei. Cl. Sci. Fis., Mat. Natur. Rend.,57, No. 6, 502–505 [1974(1975)].

    Google Scholar 

  381. S. P. Singh and B. J. Holden, “Some fixed point theorems,” Bull. Soc. R. Sci. Liege,41, Nos. 9–10, 458–461 (1972).

    Google Scholar 

  382. S. P. Singh and M. I. Riggio, “On a theorem of J. B. Diaz and F. T. Metcalf,” Atti Accad. Naz. Lincei. Cl. Sci. Fis., Mat. Natur. Rend.,53, Nos. 3–4, 246–249 [1972(1973)].

    Google Scholar 

  383. S. P. Singh and M. Veitch, “Fixed point theorems for mappings with a convexity condition,” Math. Stud.,40, 279–282 [1972(1974)].

    Google Scholar 

  384. S. P. Singh and R. K. Yadav, “On the convergence of the sequence of iterates,” Ann. Soc. Sci. Bruxelles., Ser. I,87, No. 3, 279–284 (1973).

    Google Scholar 

  385. S. P. Singh and F. Zorzitto, “On fixed point theorems in metric spaces,” Ann. Soc. Sci. Bruxelles., Ser. I,85, No. 2, 117–123 (1971).

    Google Scholar 

  386. D. R. Smart, Fixed Point Theorems, Cambridge University Press, London (1974).

    Google Scholar 

  387. S. Srivastava and K. L. Singh, “Construction of fixed point for densifying maps,” Riv. Mat. Univ. Parma,2, No. 4, 147–153 (1976).

    Google Scholar 

  388. H. Steinlein, “Über die verallgemeinerten Fixpunktindizes von iterierten verdichtender Abbildungen,” Manuscr. Math.,8, No. 3, 251–266 (1973).

    Google Scholar 

  389. H. Steinlein, “An approximation method in asymptotic fixed point theory,” Math. Ann.,211, No. 3, 199–218 (1974).

    Google Scholar 

  390. C. A. Stuart, “Self-adjoint square roots of positive self-adjoint bounded linear operators,” Proc. Edinburgh Math. Soc.,18, No. 1, 77–99 (1972).

    Google Scholar 

  391. C. A. Stuart, “The fixed point index of a differentiable (β) k-set contraction,” J. London Math. Soc.,5, No. 4, 691–696 (1972).

    Google Scholar 

  392. C. A. Stuart, “The measure on non-compactness of some linear integral operators,” Proc. R. Soc. Edinburgh,A71, No. 2, 167–179 (1973).

    Google Scholar 

  393. C. A. Stuart, “Some bifurcation theory for k-set contractions,” Proc. London Math. Soc.,27, Part 3, 531–550 (1973).

    Google Scholar 

  394. C. A. Stuart, “The principal component of solutions for nonlinear eigenvalue problems,” Boll. Unione Mat. Ital.,B13, No. 3, 726–742 (1976).

    Google Scholar 

  395. C. A. Stuart and J. F. Toland, “The fixed point index of a linear k-set contraction,” J. London Math. Soc.,6, No. 2, 317–320 (1973).

    Google Scholar 

  396. C. H. Su and V. M. Sehgal, “Some fixed point theorems for condensing multifunctions in locally convex spaces,” Proc. Am. Math. Soc.,50, 150–154 (1975).

    Google Scholar 

  397. S. Szufla, “Some remarks on ordinary differential equations in Banach spaces,” Bull. Acad. Polon. Sci. Ser. Sci. Math., Astron. Phys.,16, No. 10, 795–800 (1968).

    Google Scholar 

  398. S. Szufla, “On the existence of solutions of an ordinary differential equation in the case of Banach space,” Bull. Acad. Polon. Sci. Ser. Sci. Math., Astron. Phys.,16, No. 4, 311–315 (1968).

    Google Scholar 

  399. S. Szufla, “Measure of non-compactness and ordinary differential equations in Banach spaces,” Bull. Acad. Pol. Sci. Ser. Sci. Math., Astron. Phys.,19, No. 9, 831–835 (1971).

    Google Scholar 

  400. S. Szufla, “Structure of the solution set of ordinary differential equations in Banach space,” Bull. Acad. Pol. Sci. Ser. Sci. Math., Astron. Phys.,21, No. 2, 141–144 (1973).

    Google Scholar 

  401. S. Szufla, “On the structure of solutions sets of differential and integral equations in Banach spaces,” Ann. Pol. Math.,34, No. 2, 165–177 (1977).

    Google Scholar 

  402. S. Szufla, “On the existence of solutions of ordinary differential equations in Banach spaces,” Boll. Unione Mat. Ital.,A15, No. 3, 535–544 (1978).

    Google Scholar 

  403. L. A. Talman, “Fixed points for condensing multifunctions in metric spaces with convex structure,” Kodai Math. Semin. Repts.,29, Nos. 1–2, 62–70 (1977).

    Google Scholar 

  404. L. A. Talman, “A note on Kellogg's uniqueness theorem for fixed points,” Proc. Am. Math. Soc.,69, No. 2, 248–250 (1978).

    Google Scholar 

  405. E. Tarafdar and R. Výborný, “Fixed point theorems for condensing multivalued mapping on a locally convex topological space,” Bull. Austral. Math. Soc.,12, No. 2, 161–170 (1975).

    Google Scholar 

  406. J. W. Thomas, “A bifurcation theorem for k-set-contractions,” Pacific J. Math.,44, No. 2, 749–756 (1973).

    Google Scholar 

  407. J. W. Thomas, “The multiplicity of an operator is a special case of the topological degree for k-set contractions,” Duke Math. J.,40, No. 2, 233–240 (1973).

    Google Scholar 

  408. J. W. Thomas, “Upper and lower bounds for the number of solutions of functional equations and involving k-set contractions,” Rocky Mountain J. Math.,4, No. 1, 89–94 (1974).

    Google Scholar 

  409. R. Thompson, “An invariance property of solutions to second-order differential inequalities in ordered Banach spaces,” SIAM J. Math. Anal.,8, No. 3, 592–603 (1977).

    Google Scholar 

  410. J. F. Toland, “Global bifurcation for k-set contractions without multiplicity assumptions,” Q. J. Math.,27, No. 106, 199–216 (1976).

    Google Scholar 

  411. G. M. Vainikko, Funktionanalyses der Diskretisierungsmethoden, Teubner Verlagsges., Leipzig (1976).

    Google Scholar 

  412. A. Vignoli, “An intersection theorem in Banach spaces,” Atti Accad. Naz. Lincei. Cl. Sci. Fis., Mat. Natur. Rend.,49, Nos. 3–4, 180–183 (1970).

    Google Scholar 

  413. A. Vignoli, “Onα-contractions and surjectivity,” Boll. Unione Mat. Ital.,4, No. 3, 446–455 (1971).

    Google Scholar 

  414. A. Vignoli, “On quasibounded and nonlinear functional equations,” Atti Accad. Naz. Lincei. Cl. Sci. Fis. Fis., Mat. Natur. Rend.,50, No. 2, 114–117 (1971).

    Google Scholar 

  415. P. Volkmann, “Über die Existenz von Lösungen der Differentialgleichung u′=f(u) in einer bgeschlossenen menge, wenn f eine k-Mengenkontraktion ist,” Lect. Notes Math.,564, 496–503 (1976).

    Google Scholar 

  416. J. R. L. Webb, “Fixed point theorems for non-linear semicontractive operators in Banach spaces,” J. London Math. Soc.,1, No. 4, 683–688 (1969).

    Google Scholar 

  417. J. R. L. Webb, “A fixed point theorem and applications to functional equations in Banach spaces,” Boll. Unione Mat. Ital.,4, No. 5, 775–788 (1971).

    Google Scholar 

  418. J. R. L. Webb, “On a characterisation of k-set contractions,” Atti Accad. Naz. Lincei. Cl. Sci. Fis., Mat. Natur. Rend.,50, No. 6, 686–689 (1971).

    Google Scholar 

  419. J. R. L. Webb, “Remarks on k-set-contractions,” Boll. Unione Mat. Ital.,4, No. 4, 614–629 (1971).

    Google Scholar 

  420. J. R. L. Webb, “On degree theory for multivalued mappings and applications,” Boll. Unione Mat. Ital.,9, No. 1, 137–158 (1974).

    Google Scholar 

  421. J. R. L. Webb, “On uniqueness of topological degree for set-valued mappings,” Proc. R. Soc. Edinburgh,A74, 225–229 (1976).

    Google Scholar 

  422. R. Wolf, “Diskret kondensierende Operatorfolgen,” Math. Nachr.,80, 209–223 (1977).

    Google Scholar 

  423. H. S. F. Wong, “The topological degree of A-proper maps,” Can. J. Math.,23, No. 3, 403–412 (1971).

    Google Scholar 

  424. C. Zanco, “Some remarks on densifying mappings,” Rend. Ist. Lombardo Accad. Sci. Lett.,A111, No. 2, 342–350 (1977).

    Google Scholar 

  425. E. Zeidler, “Zur Eindeutigkeit von Fixpunktindizes für nichtkompakte Operatoren,” Math. Nachr.,72, 51–85 (1976).

    Google Scholar 

  426. E. Zeidler, Vorlesungen über nichtlineare Funktionalanalysis. I. Fixpunktsätze, Teubner Verlagsges., Leipzig (1976).

    Google Scholar 

Download references

Authors
  1. R. R. Akhmerov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. I. Kamenskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. S. Potapov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. B. N. Sadovskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Matematicheskii Analiz, Vol. 18, pp. 185–250, 1980.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Akhmerov, R.R., Kamenskii, M.I., Potapov, A.S. et al. Condensing operators. J Math Sci 18, 551–592 (1982). https://doi.org/10.1007/BF01084869

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01084869

Search

Navigation