Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
Academic Editor: Charles E. Chidume
Copyright © 2010 Somyot Plubtieng and Kamonrat Sombut. 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.
We introduce an iterative sequence and prove a weak convergence theorem for
finding a solution of a system of mixed equilibrium problems and the set of fixed points of a quasi-nonexpansive
mapping in Hilbert spaces. Moreover, we apply our result to obtain a weak convergence theorem for finding a solution of a system of mixed equilibrium problems and the set of fixed points of a nonspreading mapping. The result obtained in this paper improves and extends the recent ones announced by Moudafi (2009), Iemoto and Takahashi (2009), and many others. Using this result, we improve and unify several results
in fixed point problems and equilibrium problems.