Convergence theorems by the viscosity approximation method for equilibrium problems and variational inequality problems
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Author list: Jaiboon C., Kumam P., Humphries U.W.
Publication year: 2009
Journal: Journal of Computational Mathematics and Optimization (0972-9372)
Volume number: 5
Issue number: 1
Start page: 29
End page: 56
Number of pages: 28
ISSN: 0972-9372
Languages: English-Great Britain (EN-GB)
Abstract
In this paper, we introduce a new iterative scheme for finding the common element of the set of: fixed points of a nonexpansive mapping; equilibrium; and the variational inequality problems for α-inverse-strongly monotone mappings by the viscosity approximation method in a Hilbert spaces. We show that the sequence converges strongly to a common element of the above three sets under some parameter controlling conditions. This main theorem extends a recent result of Chen et al. [5] Su et al. [13] and Yao et al. [19] and many others. © SAS International Publications.
Keywords
Viscosity method, α-inverse-strongly monotone mappings
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