A general iterative method for addressing mixed equilibrium problems and optimization problems
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Author list: Jaiboon C., Kumam P.
Publisher: Elsevier
Publication year: 2010
Journal: Nonlinear Analysis (0362-546X)
Volume number: 73
Issue number: 5
Start page: 1180
End page: 1202
Number of pages: 23
ISSN: 0362-546X
Languages: English-Great Britain (EN-GB)
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Abstract
In this paper, we introduce a new general iterative method for finding a common element of the set of solutions of a mixed equilibrium problem (MEP), the set of fixed points of an infinite family of nonexpansive mappings {T n}n=1∞ and the set of solutions of variational inequalities for a ξ-inverse-strongly monotone mapping in Hilbert spaces. Furthermore, we establish the strong convergence theorem for the iterative sequence generated by the proposed iterative algorithm under some suitable conditions, which solves some optimization problems. Our results extend and improve the recent results of Yao et al. [Y. Yao, M.A. Noor, S. Zainab, Y.C. Liou, Mixed equilibrium problems and optimization problems, J. Math. Anal. Appl. 354 (2009) 319329; Y. Yao, M. A. Noor, Y.C. Liou, On iterative methods for equilibrium problems, Nonlinear Anal. 70 (1) (2009) 479509] and many others. © 2010 Elsevier Ltd. All rights reserved.
Keywords
Mixed equilibrium problem
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