Open Access

Strong Convergence of Cesàro Mean Iterations for Nonexpansive Nonself-Mappings in Banach Spaces

Fixed Point Theory and Applications20072007:059262

DOI: 10.1155/2007/59262

Received: 9 March 2007

Accepted: 12 September 2007

Published: 25 October 2007

Abstract

Let be a real uniformly convex Banach space which admits a weakly sequentially continuous duality mapping from to , a nonempty closed convex subset of which is also a sunny nonexpansive retract of , and a non-expansive nonself-mapping with . In this paper, we study the strong convergence of two sequences generated by and for all , where , is a real sequence in an interval , and is a sunny non-expansive retraction of onto . We prove that and converge strongly to and , respectively, as , where is a sunny non-expansive retraction of onto . The results presented in this paper generalize, extend, and improve the corresponding results of Matsushita and Kuroiwa and many others.

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Authors’ Affiliations

(1)
Department of Mathematics, Faculty of Science, Naresuan University

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Copyright

© Rabian Wangkeeree. 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.