Generalized KKM maps, maximal elements and almost fixed points

Hoonjoo Kim; Sehie Park

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J. Korean Math. Soc. 2007; 44(2): 393-406

Printed March 1, 2007

Generalized KKM maps, maximal elements and almost fixed points

Hoonjoo Kim and Sehie Park

Daebul University, Seoul National University

Abstract

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Abstract

In the framework of generalized convex spaces, we show that generalized KKM maps can be regarded as ordinary KKM maps, and obtain some applications to equilibrium result, maximal element theorems, and almost fixed point theorems on multimaps of the Zima type.

Keywords: $G$-convex space, KKM map, generalized KKM, generalized $\gamma$-quasiconvexity, maximal elements, Zima type, almost fixed point

MSC numbers: 47H10, 47H04, 49J40, 52A07, 54C60, 54H25