A new hybrid iterative method for mixed equilibrium problems and variational inequality problem for relaxed cocoercive mappings with application to optimization problems
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Publication Details
Author list: Kumam P., Jaiboon C.
Publisher: Elsevier
Publication year: 2009
Journal: Nonlinear Analysis: Hybrid Systems (1751-570X)
Volume number: 3
Issue number: 4
Start page: 510
End page: 530
Number of pages: 21
ISSN: 1751-570X
eISSN: 1878-7460
Languages: English-Great Britain (EN-GB)
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Abstract
In this paper, we introduce and study a new hybrid iterative method for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of variational inequalities for a ξ-Lipschitz continuous and relaxed (m, v)-cocoercive mappings in Hilbert spaces. Then, we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm which solves some optimization problems under some suitable conditions. Our results extend and improve the recent results of Yao et al. [Y. Yao, M.A. Noor, S. Zainab and Y.C. Liou, Mixed equilibrium problems and optimization problems, J. Math. Anal. Appl (2009). doi:10.1016/j.jmaa.2008.12.005] and Gao and Guo [X. Gao and Y. Guo, Strong convergence theorem of a modified iterative algorithm for Mixed equilibrium problems in Hilbert spaces, J. Inequal. Appl. (2008). doi:10.1155/2008/454181] and many others. © 2009 Elsevier Ltd. All rights reserved.
Keywords
Mixed equilibrium problem, Optimization problems
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