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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A monotone principle of fixed points


Author: M. R. Tasković
Journal: Proc. Amer. Math. Soc. 94 (1985), 427-432
MSC: Primary 54H25; Secondary 54C60
MathSciNet review: 787887
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Abstract: In this paper we formulate a new principle of fixed points, and we call it "monotone principle of fixed points".

A fixed point theorem for set-valued mappings in a complete metric space and some theorems on fixed points in arbitrary topological spaces are presented in this paper. Also, we describe a class of conditions sufficient for the existence of a fixed point which generalize several known results. We introduce the concept of a contraction principle and CS-convergence. With such an extension, a very general fixed point theorem is obtained to include a recent result of the author, which contains, as special cases, some results of J. Dugundji and A. Granas, F. Browder, D. W. Boyd and J. S. Wong, J. Caristi, T. L. Hicks and B. E. Rhoades, B. Fisher, W. Kirk and M. Krasnoselskij.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0787887-X
PII: S 0002-9939(1985)0787887-X
Keywords: Fixed point theorems, contraction and nonexpansive mappings, complete metric space, topological space
Article copyright: © Copyright 1985 American Mathematical Society