Article
Kyungpook Mathematical Journal 2022; 62(3): 533-555
Published online September 30, 2022
Copyright © Kyungpook Mathematical Journal.
Halpern Subgradient Method for Pseudomonotone Equilibrium Problems in Hilbert Space
Tran Van Thang∗ and Nguyen Minh Khoa
Electric Power University, Hanoi, Vietnam
e-mail : thangtv@epu.edu.vn and khoanm@epu.edu.vn
Received: November 27, 2020; Revised: June 7, 2021; Accepted: June 8, 2021
In this paper, we introduce a new algorithm for finding a solution of an equilibrium problem in a real Hilbert space. Our paper extends the single projection method to pseudomonotone variational inequalities, from a 2018 paper of Shehu et. al., to pseudomonotone equilibrium problems in a real Hilbert space. On the basis of the given algorithm for the equilibrium problem, we develop a new algorithm for finding a common solution of a equilibrium problem and fixed point problem. The strong convergence of the algorithm is established under mild assumptions. Several of fundamental experiments in finite (infinite) spaces are provided to illustrate the numerical behavior of the algorithm for the equilibrium problem and to compare it with other algorithms.
Keywords: Equilibrium problem, weakly continuous, subgradient, pseudomonotone, Halpern subgradient method