Nonlinear common fixed point properties of semitopological semigroups in uniformly convex spaces

Abstract

In this paper, we study common fixed point properties of semitopological semigroups of nonexpansive mappings in uniformly convex spaces and in Banach spaces. We prove a fixed point property for semitopological semigroups which ensures the existence of a common fixed point for any nonexpansive action of a left reversible semitopological semigroup on a nonempty bounded closed convex subset of a uniformly convex Banach space; extending a well-known result of Browder (1965). By considering weakly compact convex sets with normal structure, we are able to extend our result to general Banach spaces; generalizing some results in the literature.