Kyungpook Mathematical Journal 2022; 62(1): 89-106
Published online March 31, 2022
Copyright © Kyungpook Mathematical Journal.
An Iterative Method for Equilibrium and Constrained Convex Minimization Problems
Maryam Yazdi, Mohammad Mehdi Shabani, Saeed Hashemi Sababe*
Young Researchers and Elite Club, Malard Branch, Islamic Azad University, Malard, Iran
e-mail : email@example.com
Faculty of sciences, Imam Ali University, Tehran, Iran
e-mail : firstname.lastname@example.org
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada and Young Researchers and Elite Club, Malard Branch, Islamic Azad University, Malard, Iran
e-mail : email@example.com">firstname.lastname@example.org, email@example.com
Received: February 1, 2021; Accepted: November 8, 2021
We are concerned with finding a common solution to an equilibrium problem associated with a bifunction, and a constrained convex minimization problem. We propose an iterative fixed point algorithm and prove that the algorithm generates a sequence strongly convergent to a common solution. The common solution is identified as the unique solution of a certain variational inequality.
Keywords: Nonexpansive mapping, equilibrium problem, fixed point, convex minimization, averaged mapping, iterative method, variational inequality