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

Let X$X$ 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 _xn+1=_λn+1f(_xn)+(1−_λn+1)_Tn+1xn$x_{n+1}={\lambda }_{n+1}f\left(x_n\right)+(1-{\lambda }_{n+1})T_{n+1}{x}_n$ (where f$f$ is a generalized contraction mapping) for infinitely many nonexpansive self-mappings _T1,_T2,_T3,…$T_1,T_2,T_3,\dots$ in X$X$. We establish a strong convergence result which generalizes some results in the literature.