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Research Article | Open Access

A strong convergence theorem for solving pseudo-monotone variational inequalities and fixed point problems using subgradient extragradient method in Banach spaces

Fei Ma( ), Jun Yang, Min Yin
School of Mathematics and Statistics, Xianyang Normal University, Xianyang 712000, Shaanxi, China
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Abstract

In this paper, we introduce an algorithm for solving variational inequalities problem with Lipschitz continuous and pseudomonotone mapping in Banach space. We modify the subgradient extragradient method with a new and simple iterative step size, and the strong convergence to a common solution of the variational inequalities and fixed point problems is established without the knowledge of the Lipschitz constant. Finally, a numerical experiment is given in support of our results.

Keywords

variational inequalitiessubgradient extragradient methodfixed point problemBanach spacestrong convergence
CLC number: 65J15, 47C25, 90C33, 90C52

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AIMS Mathematics
Volume 7 Issue 4,
April 2022
Pages 5015-5028
DOI: 10.3934/math.2022279

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Cite this article:
Ma F, Yang J, Yin M. A strong convergence theorem for solving pseudo-monotone variational inequalities and fixed point problems using subgradient extragradient method in Banach spaces. AIMS Mathematics, 2022, 7(4): 5015-5028. https://doi.org/10.3934/math.2022279

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Received: 18 October 2021
Revised: 06 December 2021
Accepted: 22 December 2021
Published: 15 April 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)