SOME FIXED-POINT THEOREMS ON AN ALMOST G-CONVEX SUBSET OF A LOCALLY G-CONVEX SPACE AND ITS APPLICATIONS

Abstract

In this paper, we first obtain the generalizations of the almost fixed point theorems on the almost $G$-convex sets and the Himmelberg fixed point theorems on a locally G-convex space. Next, we invoke non-convexity of constraint regions in place of convexity and we obtain the new fixed point theorems, "Let $X$ be an almost $G$-convex subset of a locally $G$-convex space $E$. If $T \in \Gamma^* - KKM(X,X)$ is compact and closed, then $T$ has a fixed point."