Abstract
The aim of this paper is to introduce and study an inertial hybrid iterative method for solving generalized equilibrium problems involving Bregman relatively nonexpansive mappings in Banach spaces. We study the strong convergence for the proposed algorithm. Finally, we list some consequences and computational example to emphasize the efficiency and relevancy of main result.
Highlights
IntroductionInspired by the work in [20, 30, 32], we establish an inertial hybrid iterative algorithm involving Bregman relatively nonexpansive mapping to find a common solution of Generalized equilibrium problem (GEP)(1.1) and fixed point problem in a Banach space
Throughout the paper, unless otherwise stated, let Y be a reflexive Banach space with Y ∗ its dual, let K = ∅ be a closed convex subset of Y and denote by R the set of real numbers
It has been shown that the theory of equilibrium problems provides a natural, novel, and unified framework for several problems arising in nonlinear analysis, optimization, economics, finance, game theory, and engineering
Summary
Inspired by the work in [20, 30, 32], we establish an inertial hybrid iterative algorithm involving Bregman relatively nonexpansive mapping to find a common solution of GEP(1.1) and fixed point problem in a Banach space. Lemma 2.6 ([24]) Let g : Y → (–∞, +∞] be a Gateaux differentiable and totally convex function on int(domg). Since resgG,b is a Bregman firmly nonexpansive type mapping, it follows from [44, Lemma 1.3.1] that F(resgG,b) is a closed and convex subset of K. Theorem 4.1 Let K ⊆ Y with K ⊆ int(domg), where g : Y →
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