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Subgradient Extra-Gradient Algorithm for Pseudomonotone Equilibrium Problems and Fixed-Point Problems of Bregman Relatively Nonexpansive Mappings

Author

Listed:
  • Roushanak Lotfikar

    (Faculty of Basic Science, Ilam University, Ilam P.O. Box 69315-516, Iran)

  • Gholamreza Zamani Eskandani

    (Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz 51666-16471, Iran)

  • Jong-Kyu Kim

    (Department of Mathematics Education, Kyungnam University, Changwon 51767, Republic of Korea)

  • Michael Th. Rassias

    (Institute of Mathematics, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland)

Abstract

In this article, we introduce a new subgradient extra-gradient algorithm to find the common element of a set of fixed points of a Bregman relatively nonexpansive mapping and the solution set of an equilibrium problem involving a Pseudomonotone and Bregman–Lipschitz-type bifunction in reflexive Banach spaces. The advantage of the algorithm is that it is run without prior knowledge of the Bregman–Lipschitz coefficients. Finally, two numerical experiments are reported to illustrate the efficiency of the proposed algorithm.

Suggested Citation

  • Roushanak Lotfikar & Gholamreza Zamani Eskandani & Jong-Kyu Kim & Michael Th. Rassias, 2023. "Subgradient Extra-Gradient Algorithm for Pseudomonotone Equilibrium Problems and Fixed-Point Problems of Bregman Relatively Nonexpansive Mappings," Mathematics, MDPI, vol. 11(23), pages 1-21, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4821-:d:1290621
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    References listed on IDEAS

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    1. Dan Butnariu & Elena Resmerita, 2006. "Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces," Abstract and Applied Analysis, Hindawi, vol. 2006, pages 1-39, February.
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