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Abstract
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Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 649162, 9 pages
doi:10.1155/2008/649162

Strong convergence of a modified Halpern's iteration for nonexpansive mappings

Liang-Gen Hu

Department of Mathematics, Ningbo University, Ningbo 315211, China

Abstract

The purpose of this paper is to consider that a modified Halpern's iterative sequence {xn} converges strongly to a fixed point of nonexpansive mappings in Banach spaces which have a uniformly Gâteaux differentiable norm. Our result is an extension of the corresponding results.