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

被引：1

作者：

Lotfikar, Roushanak ^{[1
]}

Eskandani, Gholamreza Zamani ^{[2
]}

Kim, Jong-Kyu ^{[3
]}

Rassias, Michael Th. ^{[4
]}

机构：

[1] Ilam Univ, Fac Basic Sci, POB 69315-516, Ilam, Iran

[2] Univ Tabriz, Fac Math Sci, Dept Pure Math, Tabriz 5166616471, Iran

[3] Kyungnam Univ, Dept Math Educ, Chang Won 51767, South Korea

[4] Univ Zurich, Inst Mathemat, Winterthurerstr 190, CH-8057 Zurich, Switzerland

来源：

MATHEMATICS | 2023年 / 11卷 / 23期

关键词：

equilibrium problem; pseudomonotone bifunction; Bregman-Lipschitz-type continuity; subgradient extra-gradient method; Legendre function; STRONG-CONVERGENCE; ITERATIVE METHOD; PROXIMAL POINT; CONVEXITY; THEOREMS;

D O I：

10.3390/math11234821

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：21

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