Viscosity approximation to common fixed points of families of nonexpansive mappings with generalized contractions mappings

Abstract

Let X be a reflexive and smooth real Banach space which has a weakly sequentially continuous duality mapping. In this paper, we consider the following viscosity approximation scheme x n + 1 = λ n + 1 f ( x n ) + ( 1 − λ n + 1 ) T n + 1 x n (where f is a generalized contraction mapping) for infinitely many nonexpansive self-mappings T 1 , T 2 , T 3 , … in X . We establish a strong convergence result which generalizes some results in the literature.