Normal Structure and Common Fixed Point Properties for Semigroups of Nonexpansive Mappings in Banach Spaces
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada, T6G 2G1
Fixed Point Theory and Applications 2010, 2010:580956 doi:10.1155/2010/580956Published: 28 February 2010
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.