Normal Structure and Common Fixed Point Properties for Semigroups of Nonexpansive Mappings in Banach Spaces

Abstract

In 1965, Kirk proved that if C is a nonempty weakly compact convex subset of a Banach space with normal structure, then every nonexpansive mapping T:C→C has a fixed point. The purpose of this paper is to outline various generalizations of Kirk's fixed point theorem to semigroup of nonexpansive mappings and for Banach spaces associated to a locally compact group.