Strong convergence for maximal monotone operators, relatively quasi-nonexpansive mappings, variational inequalities and equilibrium problems

Siwaporn Saewan (), Poom Kumam () and Yeol Cho ()

Journal of Global Optimization, 2013, vol. 57, issue 4, 1299-1318

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. Copyright Springer Science+Business Media New York 2013

Keywords: Hybrid projection method; Inverse-strongly monotone operator; Variational inequality; Equilibrium problem; Relatively quasi-nonexpansive mapping; Maximal monotone operator; 47H05; 47H09; 47H10 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10898-012-0030-1

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