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

Abstract

Let E be a real uniformly convex Banach space which is also uniformly smooth. For each n = 1, 2, . . ., let Tn : E → E be a nonexpansive mapping such that ∩∞ n=1F(Tn) 6= ∅. A strong convergence theorem is proved for approximation of common fixed points of {Tn} 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.