Open Access

An approximation method for continuous pseudocontractive mappings

Journal of Inequalities and Applications20062006:28950

https://doi.org/10.1155/JIA/2006/28950

Received: 20 March 2006

Accepted: 28 May 2006

Published: 26 July 2006

Abstract

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

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Authors’ Affiliations

(1)
College of Mathematics and Information Science, Henan Normal University
(2)
Department of Mathematics, Tianjin Polytechnic University

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Copyright

© Song and Chen 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.