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

Journal of Inequalities and Applications20112011:840319

Received: 21 September 2010

Accepted: 20 January 2011

Published: 7 February 2011


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.


Variational InequalityConvergence TheoremEquilibrium ProblemMonotone MappingStrong Convergence

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Authors’ Affiliations

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


© T. Jitpeera and P. Kumam. 2011

This article is published under license to BioMed Central Ltd. 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.