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

  • 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, 𝜙A-space, L-spaces, FC-spaces, property (H), H-condition

Abstract

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

Published
2008-12-01
How to Cite
[1]
S. Park, “Remarks on KKM Maps and Fixed Point Theorems in Generalized Convex Spaces”, CUBO, vol. 10, no. 4, pp. 1–13, Dec. 2008.