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

Let XX 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 xn+1=λn+1f(xn)+(1−λn+1)Tn+1xnxn+1=λn+1f(xn)+(1−λn+1)Tn+1xn (where ff is a generalized contraction mapping) for infinitely many nonexpansive self-mappings T1,T2,T3,…T1,T2,T3,… in XX. We establish a strong convergence result which generalizes some results in the literature.