A new hybrid iterative method for mixed equilibrium problems and variational inequality problem for relaxed cocoercive mappings with application to optimization problems

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 cont...

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Vydáno v:Nonlinear analysis. Hybrid systems Ročník 3; číslo 4; s. 510 - 530
Hlavní autoři: Kumam, Poom, Jaiboon, Chaichana
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.11.2009
Témata:
Fixed point
Mixed equilibrium problem
Nonexpansive mapping
Optimization problems
Relaxed cocoercive mapping
Variational inequality
Mixed equilibrium problem
Relaxed cocoercive mapping
Variational inequality
Optimization problems
Nonexpansive mapping
Fixed point
ISSN:1751-570X
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Shrnutí: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.
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ISSN:1751-570X
DOI:10.1016/j.nahs.2009.04.001