Fixed Point Theory and Applications
Volume 2007 (2007), Article ID 31056, 15 pages
doi:10.1155/2007/31056
Research Article

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

Balwant Singh Thakur1 and Jong Soo Jung2

1School of Studies in Mathematics, Pondit Ravishankar Shukla University, Raipur 492010 CG, India
2Department of Mathematics, Dong-A University, Busan 604-714, South Korea

Received 14 March 2007; Accepted 26 May 2007

Academic Editor: Nan-Jing Huang

Copyright © 2007 Balwant Singh Thakur and Jong Soo Jung. 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.

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.