Journal of Inequalities and Applications
Volume 2011 (2011), Article ID 840319, 25 pages
Research Article

The Shrinking Projection Method for Common Solutions of Generalized Mixed Equilibrium Problems and Fixed Point Problems for Strictly Pseudocontractive Mappings

Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, Thailand

Received 21 September 2010; Revised 14 December 2010; Accepted 20 January 2011

Academic Editor: Jewgeni Dshalalow

Copyright © 2011 Thanyarat Jitpeera and Poom Kumam. 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 the shrinking hybrid projection method for finding a common element of the set of fixed points of strictly pseudocontractive mappings, the set of common solutions of the variational inequalities with inverse-strongly monotone mappings, and the set of common solutions of generalized mixed equilibrium problems in Hilbert spaces. Furthermore, we prove strong convergence theorems for a new shrinking hybrid projection method under some mild conditions. Finally, we apply our results to Convex Feasibility Problems (CFP). The results obtained in this paper improve and extend the corresponding results announced by Kim et al. (2010) and the previously known results.