Annali di Matematica Pura ed Applicata

, Volume 125, Issue 1, pp 101–115 | Cite as

Some properties of condensing maps

  • Paul Massatt


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  1. [1]
    Z. Artstein,On continuous dependence of fixed points of condensing maps, Dynamical Systems, Volume III, An International Symposium, Academic Press, New York (1976), pp. 73–75.Google Scholar
  2. [2]
    Z. Artstein,Continuous dependence of solutions of operator equations I, Trans. Math. Soc.,231, no. 1 (1977), pp. 143–166.Google Scholar
  3. [3]
    J. E. Billotti -J. P. LaSalle,Periodic dissipative processes, Bull. A.M.S.,6 (1971), pp. 1082–1089.Google Scholar
  4. [4]
    F. E. Browder,On a generalization of the Schauder fixed point theorem, Duke Math. J.,26 (1959), pp. 291–303.Google Scholar
  5. [5]
    F. E. Browder,Another generalisation of the Schauder fixed point theorem, Duke Math. J.,32 (1965), pp. 399–406.Google Scholar
  6. [6]
    W. E. Brumley,On the asymptotic behavior of solutions of differential equations of neutral type, J. D. E.7 (1970), pp. 175–188.Google Scholar
  7. [7]
    M. F. Cheng,On continuity of fixed points of collectively condensing maps, Proc. A.M.S.,63, no. 1 (1977), pp. 74–76.Google Scholar
  8. [8]
    G. D.Cooperman,α-condensing maps and dissipative systems, Ph.D. thesis, Brown University, June 1978.Google Scholar
  9. [9]
    G. Darbo,Punti uniti in transformazioni a codominio non compatto, Rend. Sem. Math. Univ. Padova,24 (1955), pp. 84–92.Google Scholar
  10. [10]
    M. Furi -M. Martelli -A. Vignoli,Contributions to the spectral theory for nonlinear operators in Banach spaces, to appear in Annali di Matematica Pura and Applicata (4),118 (1978), pp. 229–294.Google Scholar
  11. [11]
    I. Gohberg -M. G. Krein,The basic properties of defect numbers, root numbers, and indices of linear operators, Amer. Math. Soc. Trans., Series 2,43 (1960), pp. 185–264.Google Scholar
  12. [12]
    J. K. Hale,α-contractions and differential equations, Proc. Equations Differential Fon. Nonlin. (Brussels, 1975), Hermann, Paris, pp. 15–42.Google Scholar
  13. [13]
    J. K. Hale,Continuous dependence of fixed points of condensing maps, J. Math. Appl.,46 (1974), pp. 388–394.Google Scholar
  14. [14]
    J. K. Hale,Theory of functional differential equations, Appl. Math. Sci.,3, Springer-Verlag, New York, 1977.Google Scholar
  15. [15]
    J. K. Hale -J. P. LaSalle -M. Slemrod,Theory of a general class of dissipative processes, J. Math. Anal. Appl.,39 (1972), pp. 179–181.Google Scholar
  16. [16]
    J. K. Hale -O. Lopes,Fixed point theorems and dissipative processes, J. Differential Equations,13 (1973), pp. 391–402.Google Scholar
  17. [17]
    W. A. Horn,Some fixed point theorems for compact maps and flows in Banach spaces, Trans. A.M.S.,149 (1970), pp. 391–404.Google Scholar
  18. [18]
    J. L. Kelley,General Topology, Van Nostrand, Princeton, N.J., M.R.,16 (1955), p. 1136.Google Scholar
  19. [19]
    C. Kuratowski,Sur les espaces completes, Fund. Math.,15 (1930), pp. 301–309.Google Scholar
  20. [20]
    R.Leggett,Remarks on set-contractions and condensing maps, Mathematisches Institut Ruhr-Universität D-4630 Bochum, Germany, preprint.Google Scholar
  21. [21]
    N. N. Levins,Transformation theory of non-linear differential equations of the second order, Annals of Math.,45 (1944), pp. 724–737.Google Scholar
  22. [22]
    M.Martelli,Nonrepulsive fixed point theorems and applications.Google Scholar
  23. [23]
    R. D.Nussbaum,The radius of the essential spectrum, Duke Math. J.,38, no. 3 (1970).Google Scholar
  24. [24]
    R. D. Nussbaum,Some asymptotic fixed point theorems, Trans. A.M.S.,174 (1972), pp. 349–375.Google Scholar
  25. [25]
    B. N. Sadovskii,On a fixed point principle, Funktsional. Analis,4, no 2 (1967), pp. 74–76.Google Scholar
  26. [26]
    B. N. Sadovskii,Some remarks on condensing operators and measures of noncompactness, Trudy, Mat. fac Vownezh Gos. Univ., no. 1 (1970), pp. 112–124.Google Scholar
  27. [27]
    B. N. Sadovskii,Limit compact and condensing operators, Uspekhi Mat. Nauk,4 (1972), pp. 81–146= Russian Math. Surveys,27 (1972), pp. 85–146.Google Scholar
  28. [28]
    A. E. Taylor,Theorems on ascent, descent, nullity, and defect of linear operators, Math. Ann.,163 (1966), pp. 18–49.Google Scholar
  29. [29]
    B. Yood,Properties of linear transformations preserved under addition of a completely continuous transformation, Duke Math. J.,48 (1951), pp. 599–612.Google Scholar

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© Fondazione Annali di Matematica Pura ed Applicata 1980

Authors and Affiliations

  • Paul Massatt
    • 1
  1. 1.ProvidenceUSA

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