References
Alman, M.: A fixed point theorem in Banach space. Bull. Acad. Polon. Sci. C. III5, 89–92 (1957).
Borisovic, Ju. G., Sapronov, Ju. I.: A contribution to the topological theory of condensing operators. Soviet Math. Doklady9, 1304–1307 (1968).
Browder, F. E.: A new generalization of the Schauder fixed point theorem. Math. Ann.174, 285–290 (1967).
—: The fixed point theory of multi-valued mappings in topological vector spaces. Math. Ann.177, 283–301 (1968).
Danes, J.: Some fixed point theorems. Comment. Math. Univ. Carolinae9, 223–235 (1968).
Dunford, N., Schwartz, J. T.: Linear operators I. New York: Interscience 1958.
Fan, K.: Fixed point and minimax theorems in locally convex topological linear spaces. Proc. Nat. Acad. Sci. U.S.A.38, 121–126 (1952).
—: Extensions of two fixed point theorems of F. E. Browder. Math. Z.112, 234–240 (1969).
Figueiredo, D. G. de: Topics in nonlinear functional analysis. College Park, Maryland: University of Maryland Lecture Series 1967.
Furi, M., Vignoli, A.: On alpha-nonexpansive mappings and fixed points. Rend. Accad. Naz. Lincei (8)48, 195–198 (1970).
Glicksberg, I. L.: A further generalization of the Kakutani fixed point theorem, with application to Nash equilibrium points. Proc. Amer. Math. Soc.3, 170–174 (1952).
Granas, A.: Sur la notion du degré topologique pour une certaine classe de transformations multivalentes dans les espaces de Banach. Bull. Acad. Polon. Sci. Série des sci. math., astr. et phys.7, 191–194 (1959).
—: Theorem on antipodes and theorems on fixed points for a certain class of multivalued mappings in Banach spaces. Bull. Acad. Polon. Sci. Sér. sci. math. astron. phys.7, 271–275 (1959).
Halpern, B. R., Bergman, G. M.: A fixed-point theorem for inward and outward maps. Trans. Amer. Math. Soc.130, 353–358 (1968).
—: A general fixed-point theorem. Proceedings of Symposia in Pure Mathematics vol. 18 part 1, Providence, Rhode Island: Amer. Math. Soc. 1970 (114–131).
Halpern, B.: Fixed point theorems for set-valued maps in infinite dimensional spaces. Math. Ann.189, 87–98 (1970).
Hanani, H., Netanyahu, E., Reichaw-Reichbach, M.: The sphere in the image. Israel J. Math.1, 188–195 (1963).
Himmelberg, C. J., Porter, J. R., Vleck, F. S. van: Fixed point theorems for condensing multifunctions. Proc. Amer. Math. Soc.23, 635–641 (1969).
Hukuhara, M.: Sur l'application semi-continue dont la valeur est un compact convexe. Funkcialaj Ekvacioj10, 43–66 (1967).
Istratescu, V., Istratescu, A.: On the theory of fixed points for some classes of mappings III. Rend. Accad. Naz. Lincei (8)49, 43–46 (1970).
Kasriel, R. H., Nashed, M. Z.: Stability of solutions of some classes of nonlinear operator equations. Proc. Amer. Math. Soc.17, 1036–1042 (1966).
Köthe, G.: Topologische Lineare Räume I, 2. Aufl. Berlin-Heidelberg-New York: Springer 1966.
Kuratowski, K.: Topology I. Warszawa-New York: PWN-Academic Press 1966.
Lami Dozo, E.: Opérateurs Non-expansifs,P-compacts et Propriétés Géométriques de la Norme. Doctoral Dissertation: Universite Libre de Bruxelles 1970.
Lifsic, E. A., Sadovskii, B. N.: A fixed-point theorem for generalized condensing operators. Soviet Math. Doklady9, 1370–1372 (1968).
Loc, N. X.: Fixed points and openness in a locally convex space. Proc. Amer. Math. Soc.18, 987–991 (1967).
Michael, E.: A selection theorem. Proc. Amer. Math. Soc.17, 1404–1406 (1966).
Nagumo, M.: Degree of mapping in convex linear topological spaces. Amer. J. Math.73, 497–511 (1951).
Nussbaum, R.D.: The fixed point index and fixed point theorems fork-set-contractions. Doctoral Dissertation: The University of Chicago 1969.
Nussbaum, R. D.: The fixed point index for local condensing maps. To appear.
Opial, Z.: Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bull. Amer. Math. Soc.73, 591–597 (1967).
Petryshyn, W.V.: On nonlinearP-compact operators in Banach space with applications to constructive fixed-point theorems. J. Math. Analysis Appl.15, 228–242 (1966).
— Remarks on fixed point theorems and their extensions. Trans. Amer. Math. Soc.126, 43–53 (1967).
Reich, S.: Problem 5721. Amer. Math. Monthly77, 313 (1970).
Reich, S.: A fixed point theorem. Rend. Accad. Naz. Lincei, to appear.
Reichbach (Reichaw), M.: Fixed points and openness. Proc. Amer. Math. Soc.12, 734–736 (1961).
Reinermann, J.: Fixpunktsätze vom Krasnoselski-Typ. Math. Z.119, 339–344 (1971).
Sadovskii, B. N.: A fixed point principle. Functional Anal. Appl.1, 151–153 (1967).
Schaefer, H.: Über die Methode der a priori-Schranken. Math. Ann.129, 415–416 (1955).
Tychonoff, A.: Ein Fixpunktsatz, Math. Ann.111, 767–776 (1935).
Wilansky, A.: Functional analysis. New York: Blaisdell 1964.
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Reich, S. Fixed points in locally covex spaces. Math Z 125, 17–31 (1972). https://doi.org/10.1007/BF01111112
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DOI: https://doi.org/10.1007/BF01111112