Journal of Inequalities and Applications 
Volume 2006 (2006), Article ID 28950, 9 pages
doi:10.1155/JIA/2006/28950

An approximation method for continuous pseudocontractive mappings

Yisheng Song1 and Rudong Chen2

 1College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
2Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China
Received 20 March 2006; Revised 24 May 2006; Accepted 28 May 2006

Abstract

Let K be a closed convex subset of a real Banach space E, T:K→K is continuous pseudocontractive mapping, and f:K→K is a fixed L-Lipschitzian strongly pseudocontractive mapping. For any t∈(0,1), let xt be the unique fixed point of tf+(1−t)T. We prove that if T has a fixed point and E has uniformly Gâteaux differentiable norm, such that every nonempty closed bounded convex subset of K has the fixed point property for nonexpansive self-mappings, then {xt} converges to a fixed point of T as t approaches to 0. The results presented extend and improve the corresponding results of Morales and Jung (2000) and Hong-Kun Xu (2004).