Krasnoselski-Mann Iterations for Hierarchical Fixed Point Problems for a Finite Family of Nonself Mappings in Banach Spaces

Abstract

This paper deals with a method for approximating a solution of the following problem: find hierarchically a common fixed point of a finite family of nonself nonexpansive mappings with respect to a nonexpansive self mapping on a closed convex subset of a smooth and reflexive Banach space X, which admits a weakly sequentially continuous duality mapping. First, we prove a weak convergence theorem which extends and improves one recent result proved by Yao and Liou (see Inverse Problems 24 (2008), doi:10.1088/0266-5611/24/1/015015). Secondly, when the self mapping is a contraction, we prove, under different restrictions on parameters, a strong convergence result which generalize some recent results in the literature.