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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 430409, 8 pages
http://dx.doi.org/10.1155/2013/430409
Research Article

Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems

Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Received 15 October 2012; Accepted 13 December 2012

Academic Editor: Allan Peterson

Copyright © 2013 Kamonrat Sombut and Somyot Plubtieng. 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 an iterative algorithm for finding a common element of the set of fixed points of quasi-nonexpansive mappings and the solution of split feasibility problems (SFP) and systems of equilibrium problems (SEP) in Hilbert spaces. We prove that the sequences generated by the proposed algorithm converge weakly to a common element of the fixed points set of quasi-nonexpansive mappings and the solution of split feasibility problems and systems of equilibrium problems under mild conditions. Our main result improves and extends the recent ones announced by Ceng et al. (2012) and many others.