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J-variational inequalities and zeroes of a family of maximal monotone operators by sunny generalized nonexpansive retraction

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Abstract

In this paper, using generalized resolvents and retractions onto shrinking closed subsets, we present new extragradient algorithms for finding the solution of a J-variational-like inequality, the zero points of a family of maximal monotone operators, and the solution set of mixed equilibrium problems for a J-\(\alpha \)-inverse-strongly monotone-like operator in a 2-uniformly convex and 2-uniformly smooth Banach space. By introducing the new definitions, we prove strong convergence of generated iterates in the extragradient methods. Using FMINCON optimization toolbox in MATLAB, we give some numerical examples and compare them with several existence results in the literature to illustrate the usability of our results.

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Authors and Affiliations

  1. Department of Mathematics, Sahand University of Technology, Tabriz, Iran

    Zeynab Jouymandi & Fridoun Moradlou

Authors
  1. Zeynab Jouymandi
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  2. Fridoun Moradlou
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Correspondence to Fridoun Moradlou.

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Communicated by Natasa Krejic.

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Jouymandi, Z., Moradlou, F. J-variational inequalities and zeroes of a family of maximal monotone operators by sunny generalized nonexpansive retraction. Comp. Appl. Math. 37, 5358–5374 (2018). https://doi.org/10.1007/s40314-018-0640-4

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  • DOI: https://doi.org/10.1007/s40314-018-0640-4

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