Convergence theorem for mixed equilibrium problems and variational inequality problems for relaxed cocoercive mappings
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Publication Details
Author list: Wangkeeree R., Petrot N., Kumam P., Jaiboon C.
Publisher: Eudoxus Press LLC
Publication year: 2011
Journal: Journal of Computational Analysis and Applications (1521-1398)
Volume number: 13
Issue number: 3
Start page: 425
End page: 449
Number of pages: 25
ISSN: 1521-1398
Languages: English-Great Britain (EN-GB)
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Abstract
In this paper, we introduce a new iterative scheme for finding the common element of the set of common fixed points of countable family of nonexpansive mappings, the set of solution of a mixed equilibrium problem and the set of solution of the variational inequality problems for a relaxed (u, v)-cocoercive and μ-Lipschitz continuous mapping in Hilbert spaces. We show that the sequence converges strongly to a common element of the above three sets under some parameter controlling conditions. Our results improve and extend the recent ones announced by [Y.J. Cho, X.Q. Qin, M. Kang, Some results for equilibrium problems and fixed point problems in Hilbert spaces, J. Comput. Anal. Appl. 11(2009) 294-316] and many others. © 2011 EUDOXUS PRESS, LLCAll rights reserved.
Keywords
Fixed points, Mixed equilibrium problem, Relaxed cocoercive mapping
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