APPROXIMATION OF COMMON FIXED POINTS OF FAMILIES OF NONEXPANSIVE MAPPINGS*

Abstract

Let $X$ be a reflexive and smooth Banach space which has a weakly sequentially continuous duality mapping. We consider in this paper the iteration scheme $x_{n+1}=\lambda_{n+1}y+(1-\lambda_{n+1})T_{n+1}x_n$ for infinitely many nonexpansive maps $T_1,T_2,T_3,...$ in $X$ as well as for finitely many nonexpansive retraction. We establish several strong convergence results which generalize [10, Theorem 3.3] and [10, Theorem 4.1] from Hilbert space setting to Banach space setting.