Journal of Applied Mathematics
Volume 2012 (2012), Article ID 136134, 12 pages
http://dx.doi.org/10.1155/2012/136134
Research Article

Strong Convergence Theorems for a Countable Family of Total Quasi- 𝝓 -Asymptotically Nonexpansive Nonself Mappings

Liang-cai Zhao1 and Shih-sen Chang2

1College of Mathematics, Yibin University, Yibin 644000, China
2College of Statistics and Mathematics, Yunnan University of Finance and Economics, Yunnan, Kunming 650221, China

Received 3 June 2012; Revised 22 July 2012; Accepted 23 July 2012

Academic Editor: Naseer Shahzad

Copyright © 2012 Liang-cai Zhao and Shih-sen Chang. 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 introduce a class of total quasi-ϕ-asymptotically nonexpansive-nonself mappings and to study the strong convergence under a limit condition only in the framework of Banach spaces. As an application, we utilize our results to study the approximation problem of solution to a system of equilibrium problems. The results presented in the paper extend and improve the corresponding results announced by some authors recently.