The construction of a fixed point for certain families of mappings

Abstract

It is shown that for K a nonempty convex closed and bounded subset of a uniformly convex Banach space, and for F a left reversible semigroup of self mappings of K , with F satisfying a condition weaker than eventually nonexpansive, F has a common fixed point. Unlike previous solutions to problems of this type, the proof is constructive and the fixed point is determined apriori. The fixed point thus obtained is characterized for the commutative eventually nonexpansive case