A fixed point theorem for non-expansive mappings on star-shaped domains (Q1188339)

This article is devoted to generalizations and modifications of the classical results by Browder, Göhde and Kirk about fixed points of non- expansive mappings an star-shaped domains. A new version of the Browder- Göhde-Kirk theorem, which holds true on star-shaped subsets of a reflexive space with the Kadec-Klee property with some applications and an iteration scheme to construct the corresponding fixed point, are presented. At the end of the paper two characterizations of inner product spaces are obtained.