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Journal of Applied Mathematics
Volume 2012, Article ID 185104, 17 pages
http://dx.doi.org/10.1155/2012/185104
Research Article

Convergence of an Iterative Algorithm for Common Solutions for Zeros of Maximal Accretive Operator with Applications

1Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, Thailand
2Department of Mathematics Education and RINS, Gyeongsang National University, Chinju 660-701, Republic of Korea

Received 18 November 2011; Accepted 30 December 2011

Academic Editor: Yeong-Cheng Liou

Copyright © 2012 Uamporn Witthayarat 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 aim of this paper is to introduce an iterative algorithm for finding a common solution of the sets (A+M2)1(0) and (B+M1)1(0), where M is a maximal accretive operator in a Banach space and, by using the proposed algorithm, to establish some strong convergence theorems for common solutions of the two sets above in a uniformly convex and 2-uniformly smooth Banach space. The results obtained in this paper extend and improve the corresponding results of Qin et al. 2011 from Hilbert spaces to Banach spaces and Petrot et al. 2011. Moreover, we also apply our results to some applications for solving convex feasibility problems.