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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 539061, 11 pages
http://dx.doi.org/10.1155/2013/539061
Research Article

Strong Convergence of a General Iterative Method for a Countable Family of Nonexpansive Mappings in Banach Spaces

1Department of Information Management, Yuan Ze University, Chungli 32003, Taiwan
2Department of Mathematics, Yasouj University, Yasouj 75918, Iran
3Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 804, Taiwan

Received 22 August 2013; Accepted 7 September 2013

Academic Editor: Chi-Ming Chen

Copyright © 2013 Chin-Tzong Pang and Eskandar Naraghirad. 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

We introduce a general algorithm to approximate common fixed points for a countable family of nonexpansive mappings in a real Banach space. We prove strong convergence theorems for the sequences produced by the methods and approximate a common fixed point of a countable family of nonexpansive mappings which solves uniquely the corresponding variational inequality. Furthermore, we apply our results for finding a zero of an accretive operator. It is important to state clearly that the contribution of this paper in relation with the previous works (Marino and Xu, 2006) is a technical method to prove strong convergence theorems of a general iterative algorithm for an infinite family of nonexpansive mappings in Banach spaces. Our results improve and generalize many known results in the current literature.