Strong convergence theorems of iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems

Authors:
Jian-Wen Peng;Jen-Chih Yao
Affiliations:
College of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, PR China;Department of Applied Mathematics, National Sun Yat-sen University Kaohsiung, 804, Taiwan, ROC
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2009

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Abstract

In this paper, a new iterative scheme based on the extragradient method for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of a family of finitely nonexpansive mappings and the set of solutions of the variational inequality for a monotone, Lipschitz continuous mapping is proposed. A strong convergence theorem for this iterative scheme in Hilbert spaces is established. Applications to optimization problems are given.