Open Access

Weak and Strong Convergence of Multistep Iteration for Finite Family of Asymptotically Nonexpansive Mappings

Fixed Point Theory and Applications20072007:031056

DOI: 10.1155/2007/31056

Received: 14 March 2007

Accepted: 26 May 2007

Published: 29 July 2007

Abstract

Strong and weak convergence theorems for multistep iterative scheme with errors for finite family of asymptotically nonexpansive mappings are established in Banach spaces. Our results extend and improve the corresponding results of Chidume and Ali (2007), Cho et al. (2004), Khan and Fukhar-ud-din (2005), Plubtieng et al.(2006), Xu and Noor (2002), and many others.

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Authors’ Affiliations

(1)
School of Studies in Mathematics, Pondit Ravishankar Shukla University
(2)
Department of Mathematics, Dong-A University

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Copyright

© B. S. Thakur and J. S. Jung. 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.