Strong convergence for maximal monotone operators, relatively quasi-nonexpansive mappings, variational inequalities and equilibrium problems
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Publication Details
Author list: Saewan S., Kumam P., Cho Y.J.
Publisher: Springer
Publication year: 2013
Journal: Journal of Global Optimization (0925-5001)
Volume number: 57
Issue number: 4
Start page: 1299
End page: 1318
Number of pages: 20
ISSN: 0925-5001
eISSN: 1573-2916
Languages: English-Great Britain (EN-GB)
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Abstract
In this paper, we introduce a new hybrid iterative scheme for finding a common element of the set of zeroes of a maximal monotone operator, the set of fixed points of a relatively quasi-nonexpansive mapping, the sets of solutions of an equilibrium problem and the variational inequality problem in Banach spaces. As applications, we apply our results to obtain strong convergence theorems for a maximal monotone operator and quasi-nonexpansive mappings in Hilbert spaces and we consider a problem of finding a minimizer of a convex function. ฉ 2012 Springer Science+Business Media New York.
Keywords
Inverse-strongly monotone operator, Relatively quasi-nonexpansive mapping
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