Inertial Iterative Method for Generalized Mixed Equilibrium Problem and Fixed Point Problem

Vahid Darvish; Grace Nnennaya Ogwo; Olawale Kazeem Oyewole; Hammed Anuoluwapo Abass; Amirbek Aminovich Ikramov

doi:10.29020/nybg.ejpam.v18i3.6173

Inertial Iterative Method for Generalized Mixed Equilibrium Problem and Fixed Point Problem

Vahid Darvish
, Grace Nnennaya Ogwo^*
, Olawale Kazeem Oyewole
, Hammed Anuoluwapo Abass
, Amirbek Aminovich Ikramov

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper, we study the generalized mixed equilibrium problem and the fixed point problem. We propose an inertial iterative method for approximating the common solution of a generalized mixed equilibrium problem of a monotone mapping and a fixed point problem for a Bregman strongly nonexpansive mapping in the framework of real reflexive Banach spaces. Under certain mild conditions, we obtain a strong convergence result of the proposed method. Finally, we present numerical examples to illustrate the applicability of our method.

Original language	English
Article number	6173
Journal	European Journal of Pure and Applied Mathematics
Volume	18
Issue number	3
DOIs	https://doi.org/10.29020/nybg.ejpam.v18i3.6173
Publication status	Published - Jul 2025
Externally published	Yes

Keywords

Bregman strongly nonexpansive mapping
Generalized mixed equilibrium problem
fixed point problem
inertial technique

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10.29020/nybg.ejpam.v18i3.6173

Cite this

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title = "Inertial Iterative Method for Generalized Mixed Equilibrium Problem and Fixed Point Problem",

abstract = "In this paper, we study the generalized mixed equilibrium problem and the fixed point problem. We propose an inertial iterative method for approximating the common solution of a generalized mixed equilibrium problem of a monotone mapping and a fixed point problem for a Bregman strongly nonexpansive mapping in the framework of real reflexive Banach spaces. Under certain mild conditions, we obtain a strong convergence result of the proposed method. Finally, we present numerical examples to illustrate the applicability of our method.",

keywords = "Bregman strongly nonexpansive mapping, Generalized mixed equilibrium problem, fixed point problem, inertial technique",

author = "Vahid Darvish and Ogwo, \{Grace Nnennaya\} and Oyewole, \{Olawale Kazeem\} and Abass, \{Hammed Anuoluwapo\} and Ikramov, \{Amirbek Aminovich\}",

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T1 - Inertial Iterative Method for Generalized Mixed Equilibrium Problem and Fixed Point Problem

AU - Darvish, Vahid

AU - Ogwo, Grace Nnennaya

AU - Oyewole, Olawale Kazeem

AU - Abass, Hammed Anuoluwapo

AU - Ikramov, Amirbek Aminovich

PY - 2025/7

Y1 - 2025/7

N2 - In this paper, we study the generalized mixed equilibrium problem and the fixed point problem. We propose an inertial iterative method for approximating the common solution of a generalized mixed equilibrium problem of a monotone mapping and a fixed point problem for a Bregman strongly nonexpansive mapping in the framework of real reflexive Banach spaces. Under certain mild conditions, we obtain a strong convergence result of the proposed method. Finally, we present numerical examples to illustrate the applicability of our method.

AB - In this paper, we study the generalized mixed equilibrium problem and the fixed point problem. We propose an inertial iterative method for approximating the common solution of a generalized mixed equilibrium problem of a monotone mapping and a fixed point problem for a Bregman strongly nonexpansive mapping in the framework of real reflexive Banach spaces. Under certain mild conditions, we obtain a strong convergence result of the proposed method. Finally, we present numerical examples to illustrate the applicability of our method.

KW - Bregman strongly nonexpansive mapping

KW - Generalized mixed equilibrium problem

KW - fixed point problem

KW - inertial technique

UR - https://www.scopus.com/pages/publications/105013602650

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DO - 10.29020/nybg.ejpam.v18i3.6173

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VL - 18

JO - European Journal of Pure and Applied Mathematics

JF - European Journal of Pure and Applied Mathematics

IS - 3

M1 - 6173

ER -

Inertial Iterative Method for Generalized Mixed Equilibrium Problem and Fixed Point Problem

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Keywords

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