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Journal of Applied Mathematics
Volume 2012, Article ID 235474, 30 pages
http://dx.doi.org/10.1155/2012/235474
Research Article

Viscosity Approximations by the Shrinking Projection Method of Quasi-Nonexpansive Mappings for Generalized Equilibrium Problems

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

Received 16 July 2012; Accepted 27 August 2012

Academic Editor: Juan Torregrosa

Copyright © 2012 Rabian Wangkeeree and Nimit Nimana. 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 viscosity approximations by using the shrinking projection method established by Takahashi, Takeuchi, and Kubota, for finding a common element of the set of solutions of the generalized equilibrium problem and the set of fixed points of a quasi-nonexpansive mapping. Furthermore, we also consider the viscosity shrinking projection method for finding a common element of the set of solutions of the generalized equilibrium problem and the set of fixed points of the super hybrid mappings in Hilbert spaces.