Normal Structure and Common Fixed Point Properties for Semigroups of Nonexpansive Mappings in Banach Spaces
Anthony To‐Ming Lau · Fixed Point Theory and Applications · 2010
Abstract In 1965, Kirk proved that if "Equation missing" is a nonempty weakly compact convex subset of a Banach space with normal structure, then every nonexpansive mapping "Equation missing" 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.