A New Extragradient-Viscosity Method for a Variational Inequality, an Equilibrium Problem, and a Fixed Point Problem

Maryam Yazdi and Saeed Hashemi Sababe ()
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Maryam Yazdi: Young Researchers and Elite Club, Malard Branch, Islamic Azad University, Malard MX7C+G74, Iran
Saeed Hashemi Sababe: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2R3, Canada

Mathematics, 2024, vol. 12, issue 22, 1-19

Abstract: In this research article, we introduce a novel iterative approach that builds upon a two-step extragradient-viscosity method. This method aims to find a common element among the solution set of a variational inequality, an equilibrium problem, and the set of common fixed points from a countable family of demicontractive mappings in a Hilbert space. We offer a robust convergence theorem for the proposed iterative scheme, considering certain well-conditioned parameters. Our findings represent an improvement over similar results already available in the existing literature. Furthermore, we demonstrate the applicability of our main result to W-mappings. Lastly, we present two numerical examples to exhibit the consistency and accuracy of our devised scheme.

Keywords: equilibrium problem; variational inequality; extragradient method; iterative method; fixed point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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