Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada
Academic Editor: Mohamed A. Khamsi
Copyright © 2010 Anthony To-Ming Lau. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In 1965, Kirk proved that if is a nonempty weakly compact convex subset of a Banach space with normal structure, then every nonexpansive mapping 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.