Inertial Iterative Method for Generalized Mixed Equilibrium Problem and Fixed Point Problem
Vahid DarvishDepartment of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing ChinaGrace Nnennaya OgwoSchool of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, ChinaOyewole Kazeem OyewoleDepartment of Mathematics and Statistics, Tshwane University of Technology, PMB 007, Arcadia, Pretoria, South AfricaHammed Anuoluwapo AbassDepartment of Mathematics and Applied Mathematics, Sefako Makgato Health Science University, P.O. Box 94, Pretoria 0204, South AfricaAmirbek Aminovich IkramovCenter of Research and Innovation, Asia International University, Yangiobod MFY, G‘ijduvon Street, House 74, Bukhara, Uzbekistan
2025en
ABI
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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