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J-nonexpansive mappings in uniform spaces and applications

Published online by Cambridge University Press:  17 April 2009

Vasil G. Angelov
Vasil G. Angelov
Affiliation:
Department of Mathematics, Higher Mining and Geological Institute, 1156 Sofia, Bulgaria
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Abstract

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The purpose of the paper is to introduce a class of “j-nonexpansive” mappings and to prove fixed point theorems for such mappings. They naturally arise in the existence theory of functional differential equations. These mappings act in spaces without specific geometric properties as, for instance, uniform convexity. Critical examples are given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 2 , April 1991 , pp. 331 - 339
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Angelov, V.G., ‘Fixed point theorems in uniform spaces and applications’, Czechoslovak Math. Journal 37 (1987), 19–33.CrossRefGoogle Scholar
[2]Browder, F.E., ‘Nonexpansive nonlinear operators in a Banach space’, Proc. Nat. Acad. Sci. 54 (1965), 1041–1044.CrossRefGoogle Scholar
[3]Deimling, K., Nonlinear functional analysis (Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1985).CrossRefGoogle Scholar
[4]Edelstein, M., ‘On fixed and periodic points under contractive mappings’, J. London Math. Soc. 37 (1962), 74–89.CrossRefGoogle Scholar
[5]Edelstein, M., ‘On nonexpansive mappings of uniform spaces’, Indag. Math. 27 (1965), 47–51.CrossRefGoogle Scholar
[6]Gohde, D., ‘Zum Prinzip der Kontraktiven Abbildung’, Math. Nachr. 30 (1965), 251–258.CrossRefGoogle Scholar
[7]Kirk, W.A., ‘A fixed point theorem for mappings which do not increase distances’, Amer. Math. Monthly 72 (1965), 1004–1006.CrossRefGoogle Scholar
[8]Kirk, W.A., ‘Nonexpansive mappings and normal structure in Banach spaces’, in Proc. Res. Workshop on Banach spaces theory, pp. 1–15 (The University of Iowa, 1981).Google Scholar
[9]Kirk, W.A., ‘Fixed point theory for nonexpansive mappings’, in Lecture Notes in Mathematics 886, pp. 484–505 (Springer-Verlag, Berlin, Heidelberg, New York, 1981).Google Scholar
[10]Kwapisz, M., ‘On the existence and uniqueness of L−integrable solutions of a certain integral-functional equations’, Funkcial. Ekvac. 19 (1976), 191–202.Google Scholar
[11]Reinermann, J. and Stallbohm, V., ‘Eine Anwndung des Edelsteinschen Fixpunktsatzes auf Integralgleichungen vom Abel-Liouvilleschen Type’, Arch. Mathematik, XXII (1971), 642–647.CrossRefGoogle Scholar
[12]Srivastava, P. and Srivastava, S.C., ‘Fixed point theorems for nonexpansive mappings in a locally convex space’, Bull. Austral. Math. Soc. 20 (1979), 179–190.CrossRefGoogle Scholar
[13]Taylor, W.W., ‘Fixed point theorems for nonexpansive mappings in linear topological spaces’, J. Math. Anal. Appl 440 (1972), 164–173.CrossRefGoogle Scholar
[14]Weil, A., Sur les espaces a structure uniforms et sur la topologie generale (Hermann, Paris, 1938).Google Scholar