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

Authors

  • Vahid Darvish Department of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing China
  • Grace Nnennaya Ogwo School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China
  • Oyewole Kazeem Oyewole Department of Mathematics and Statistics, Tshwane University of Technology, PMB 007, Arcadia, Pretoria, South Africa
  • Hammed Anuoluwapo Abass Department of Mathematics and Applied Mathematics, Sefako Makgato Health Science University, P.O. Box 94, Pretoria 0204, South Africa
  • Amirbek Aminovich Ikramov Center of Research and Innovation, Asia International University, Yangiobod MFY, G‘ijduvon Street, House 74, Bukhara, Uzbekistan

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6173

Keywords:

Generalized mixed equilibrium problem, Fixed point problem, Inertial method

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.

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Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Functional Analysis

License

Copyright (c) 2025 Vahid Darvish, Grace Nnennaya Ogwo, Oyewole Kazeem Oyewole, Hammed Anuoluwapo Abass, Amirbek Aminovich Ikramov

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How to Cite

Inertial Iterative Method for Generalized Mixed Equilibrium Problem and Fixed Point Problem. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6173. https://doi.org/10.29020/nybg.ejpam.v18i3.6173