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A Strong Convergence Theorem for Solving an Equilibrium Problem and a Fixed Point Problem Using the Bregman Distance

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Abstract

In this paper, using the Bregman distance, we introduce a new projection-type algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points. Then the strong convergence of the sequence generated by the algorithm will be established under suitable conditions. Finally, using MATLAB software, we present a numerical example to illustrate the convergence performance of our algorithm.

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Authors and Affiliations

  1. Department of Mathematics, Payame Noor University, P. O. Box 19395-4697, Tehran, Iran

    Mostafa Ghadampour

  2. Department of Mathematics, Lorestan University, Khoramabad, Lorestan, Iran

    Ebrahim Soori

  3. Department of Mathematics, Texas A &M University-Kingsville, 700 University Blvd., MSC 172, Kingsville, TX, USA

    Ravi P. Agarwal

  4. School of Mathematics, Statistics, National University of Ireland, Galway, Ireland

    Donal O’Regan

Authors
  1. Mostafa Ghadampour
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  2. Ebrahim Soori
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  3. Ravi P. Agarwal
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  4. Donal O’Regan
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Correspondence to Ebrahim Soori.

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Communicated by Firdaus E. Udwadia.

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Ghadampour, M., Soori, E., Agarwal, R.P. et al. A Strong Convergence Theorem for Solving an Equilibrium Problem and a Fixed Point Problem Using the Bregman Distance. J Optim Theory Appl 195, 854–877 (2022). https://doi.org/10.1007/s10957-022-02110-2

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  • DOI: https://doi.org/10.1007/s10957-022-02110-2

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