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

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  • Siwaporn Saewan
  • Poom Kumam
  • Yeol Cho

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

Suggested Citation

  • Siwaporn Saewan & Poom Kumam & Yeol Cho, 2013. "Strong convergence for maximal monotone operators, relatively quasi-nonexpansive mappings, variational inequalities and equilibrium problems," Journal of Global Optimization, Springer, vol. 57(4), pages 1299-1318, December.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:4:p:1299-1318
    DOI: 10.1007/s10898-012-0030-1
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    References listed on IDEAS

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    1. Xiaolong Qin & Shin Kang & Yeol Cho, 2010. "Approximating zeros of monotone operators by proximal point algorithms," Journal of Global Optimization, Springer, vol. 46(1), pages 75-87, January.
    2. Ying Liu, 2010. "Strong convergence theorems for variational inequalities and relatively weak nonexpansive mappings," Journal of Global Optimization, Springer, vol. 46(3), pages 319-329, March.
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