A general iterative method for addressing mixed equilibrium problems and optimization problems |
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Authors: | Chaichana Jaiboon |
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Affiliation: | a Department of Mathematics, Faculty of Applied Liberal Arts, Rajamangala University of Technology Rattanakosin (RMUTR), Bangkok 10100, Thailand b Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand |
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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 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) 319-329; Y. Yao, M. A. Noor, Y.C. Liou, On iterative methods for equilibrium problems, Nonlinear Anal. 70 (1) (2009) 479-509] and many others. |
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Keywords: | 49J30 49J40 47H09 47H10 47H17 49M05 90C99 |
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