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

Mostafa Ghadampour; Ebrahim Soori; Ravi P. Agarwal; Donal O’Regan

doi:10.1007/s10957-022-02110-2

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

Mostafa Ghadampour, Ebrahim Soori, Ravi P. Agarwal, Donal O’Regan

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

4 Citations (Scopus)

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.

Original language	English
Pages (from-to)	854-877
Number of pages	24
Journal	Journal of Optimization Theory and Applications
Volume	195
Issue number	3
DOIs	https://doi.org/10.1007/s10957-022-02110-2
Publication status	Published - Dec 2022

Keywords

Asymptotical fixed point
Bregman nonexpansive mapping
Fixed point problem
Fréchet differentiable
Variational inequality

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10.1007/s10957-022-02110-2

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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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author = "Mostafa Ghadampour and Ebrahim Soori and Agarwal, \{Ravi P.\} and Donal O{\textquoteright}Regan",

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AU - O’Regan, Donal

PY - 2022/12

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KW - Asymptotical fixed point

KW - Bregman nonexpansive mapping

KW - Fixed point problem

KW - Fréchet differentiable

KW - Variational inequality

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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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Keywords

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