Viscosity Approximation Methods in Reflexive Banach Spaces

Abstract

In this paper, we study viscosity approximation methods in re exive Banach spaces. Let X be a re exive Banach space which admits a weakly sequentially continuous duality mapping  a nonempty closed convex subset of X, hn, where  a sequence of contractions on C and Tn ,  for  a nite family of commuting nonexpansive mappings on C. We show that under appropriate conditions on  the explicit iterative sequence  dened by                         where  converges strongly to a common xed point  We consequently show that the results is true for an innite family  of commuting nonexpansive mapping on C