A monotone principle of fixed points

Tasković, M. R.

doi:10.1090/S0002-9939-1985-0787887-X

A monotone principle of fixed points
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Proc. Amer. Math. Soc. 94 (1985), 427-432 Request permission

Correction: Proc. Amer. Math. Soc. 122 (1994), 643-645.

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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Some theorems on fixed point and its applications

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