The homotopic invariance for fixed points of set-valued mappings in banach spaces

Abstract

We obtain the homotopic invariance for fixed points of set-valued contractions and nonexpansive mappings whose domain is a bounded nonexpansive retract and nonempty interior subset of a uniformly convex Banach space. This gives a partial answer to a problem posed by Sims, Xu and Yuan (2001). © 2013 Bancha Panyanak.