Invariant Submeans and Semigroups of Nonexpansive Mappings on Banach Spaces with Normal Structure

In this paper we study the relation between invariant submean and normal structure in a Banach space. This is used to give an improvement and different proof of a fixed point theorem of Lim (also of Belluce and Kirk for commutative semigroups) for left reversible semigroup of nonexpansive mappings on weakly compact convex subsets of a Banach space with normal structure.