Fixed Point Theory and Applications
Volume 2006 (2006), Article ID 70830, 8 pages
doi:10.1155/FPTA/2006/70830

Approximation common fixed point of asymptotically quasi-nonexpansive-type mappings by the finite steps iterative sequences

Jing Quan,1 Shih-Sen Chang,2 and Xian Jun Long1

1Department of Mathematics, Chongqing Normal University, Chongqing 400047, China
2Department of Mathematics, Yibin University, Yibin 644007, Sichuan, China

Received 26 December 2005; Accepted 11 March 2006

Copyright © 2006 Jing Quan et al. 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

The purpose of this paper is to study sufficient and necessary conditions for finite-step iterative sequences with mean errors for a finite family of asymptotically quasi-nonexpansive and type mappings in Banach spaces to converge to a common fixed point. The results presented in this paper improve and extend the recent ones announced by Ghost-Debnath, Liu, Xu and Noor, Chang, Shahzad et al., Shahzad and Udomene, Chidume et al., and all the others.