Open Access

A New Iterative Algorithm for Approximating Common Fixed Points for Asymptotically Nonexpansive Mappings

Fixed Point Theory and Applications20072007:064874

DOI: 10.1155/2007/64874

Received: 28 February 2007

Accepted: 13 April 2007

Published: 21 May 2007

Abstract

Suppose that is a nonempty closed convex subset of a real uniformly convex and smooth Banach space with as a sunny nonexpansive retraction. Let be two weakly inward and asymptotically nonexpansive mappings with respect to with sequences , , respectively. Suppose that is a sequence in generated iteratively by , , for all , where , , and are three real sequences in for some which satisfy condition . Then, we have the following. (1) If one of and is completely continuous or demicompact and , then the strong convergence of to some is established. (2) If is a real uniformly convex Banach space satisfying Opial's condition or whose norm is Fréchet differentiable, then the weak convergence of to some is proved.

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Authors’ Affiliations

(1)
Department of Applied Mathematics, North China Electric Power University
(2)
Department of Mathematics Education and RINS, College of Natural Sciences, Gyeongsang National University

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Copyright

© H. Y. Zhou et al. 2007

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.