STRONG CONVERGENCE TO COMMON FIXED POINTS OF A FINITE FAMILY OF ASYMPTOTICALLY NONEXPANSIVE MAP

Abstract

Suppose $E$ is a real Banach space with uniform normal structure and suppose $E$ has a uniformly Gateaux differentiable norm. Let $C$ be a nonempty closed convex and bounded subset of $E$. Let $T_1,T_2,\cdots T_r: C \to C$ be a finite family of asymptotically nonexpansive mappings. In this paper, we suggest and analyze an iterative algorithm for a finite family of asymptotically nonexpansive mappings $\{T_i\}_{i=1}^r$. We show the convergence of the proposed algorithm to a common fixed point $p \in \cap_{i=1}^{r} F(T_i)$ which is the unique solution of some variational inequality. Our results can be considered as an refinement and improvement of many known results.