Remarks on KKM Maps and Fixed Point Theorems in Generalized Convex Spaces

Sehie Park

Remarks on KKM Maps and Fixed Point Theorems in Generalized Convex Spaces

Authors

Sehie Park The National Academy of Sciences, Republic of Korea, Department of Mathematical Sciences, Seoul National University, Seoul 151–747, Korea.

Keywords:

Abstract convex space, generalized (G-) convex space, ðœ™A-space, L-spaces, FC-spaces, property (H), H-condition

Abstract

Various types of ðœ™_A-spaces (X, D; {ðœ™_A}_{AâˆˆâŒ©DâŒª}) are simply G-convex spaces. Various types of generalized KKM maps on ðœ™_A-spaces are simply KKM maps on G-convex spaces. Therefore, our G-convex space theory can be applied to various types of ðœ™_A-spaces. As such examples, we obtain KKM type theorems and a very general fixed point theorem on ðœ™_A-spaces.