An extragradient method for relaxed cocoercive variational inequality and equilibrium problems
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Author list: Jaiboon C., Kumam P., Humphries U.W.
Publisher: Springer Verlag (Germany)
Publication year: 2009
Journal: Analysis in Theory and Applications (1672-4070)
Volume number: 25
Issue number: 4
Start page: 381
End page: 400
Number of pages: 20
ISSN: 1672-4070
Languages: English-Great Britain (EN-GB)
Abstract
The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of an equilibrium problem and the set of solutions of the variational inequality problem for a relaxed cocoercive and Lipschitz continuous mapping in Hilbert spaces. Then, we show that the sequence converges strongly to a common element of the above three sets under some parameter controlling conditions, which are connected with Yao, Liou, Yao[17], Takahashi[12] and many others. ฉ 2009 Editorial Board of Analysis in Theory and Applications and Springer Berlin Heidelberg.
Keywords
Relaxed cocoercive mapping
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