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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 120172, 22 pages
http://dx.doi.org/10.1155/2014/120172
Research Article

Hybrid Extragradient-Like Viscosity Methods for Generalized Mixed Equilibrium Problems, Variational Inclusions, and Optimization Problems

1Department of Mathematics, Shanghai Normal University, Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, China
2Department of Applied Mathematics, National Hsinchu University of Education, Hsinchu 30033, Taiwan
3Department of Information Management, Yuan Ze University, Chung-Li 32003, Taiwan

Received 20 November 2013; Accepted 20 December 2013; Published 9 February 2014

Academic Editor: Erdal Karapinar

Copyright © 2014 Lu-Chuan Ceng et al. 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 and analyze a new hybrid extragradient-like viscosity iterative algorithm for finding a common solution of a generalized mixed equilibrium problem, a finite family of variational inclusions for maximal monotone and inverse strongly monotone mappings, and a fixed point problem of infinitely many nonexpansive mappings in a real Hilbert space. Under some mild conditions, we prove the strong convergence of the sequence generated by the proposed algorithm to a common solution of these three problems which also solves an optimization problem.