Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 580956, 14 pages
doi:10.1155/2010/580956
Normal structure and common fixed point properties for semigroups of nonexpansive mappings in Banach spaces
Anthony To-Ming Lau
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada
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.