Approximation of Fixed Points of Nonexpansive Mappings by Modified Krasnoselski-Mann Iterative Algorithm in Banach Space

Yekini Shehu, G.C. Ugwunnadi

Abstract

Let $E$ be a realuniformly convex Banach space which is also uniformly smooth. For each $n=1,2,\ldots$, let $T_n:E\rightarrow E$ be a nonexpansive mapping such that $\cap_{n=1}^\infty F(T_n)\neq\emptyset.$ A strong convergence theorem is proved for approximation of common fixed points of $\{T_n\}$ using a modified Krasnoselki-Mann iterative algorithm introduced by Yao et al. [Y. Yao, H. Zhou, Y.C. Liou, Strong convergence of a modified Krasnoselski-Mann iterative algorithm for nonexpansive mappings, J. Appl. Math. Comput. 29 (2009) 383--389]. As  applications, we prove strong convergence theorems for approximation of common zeroes of a finite family of continuous accretive mappings of $E$ into $E$ and approximation of common fixed point (assuming existence) of a finite family of continuous pseudocontractive mappings in a real uniformly convex and uniformly smooth Banach space. Our result extends many important recent results in the literature.