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Article

Solutions for the Nonlinear Mixed Variational Inequality Problem in the System

Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia
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Author to whom correspondence should be addressed.
Symmetry 2024, 16(7), 796; https://doi.org/10.3390/sym16070796
Submission received: 16 April 2024 / Revised: 10 May 2024 / Accepted: 19 June 2024 / Published: 25 June 2024
(This article belongs to the Special Issue Computational Mathematics and Its Applications in Numerical Analysis)

Abstract

Our paper proposes a system of nonlinear mixed variational inequality problems (SNMVIPs) on Banach spaces. Under suitable assumptions, using the K-Fan fixed point theorem and Minty techniques, we demonstrate that the solution set to the SNMVIP is nonempty, weakly compact, and unique. Additionally, we suggest a stability result for the SNMVIPs by perturbing the duality mappings. Furthermore, we present an optimal control problem that is governed by the SNMVIPs and show that it can be solved.
Keywords: system of nonlinear mixed variational inequality problem; inverse relaxed monotonicity; existence; uniqueness; stability; optimal control problem system of nonlinear mixed variational inequality problem; inverse relaxed monotonicity; existence; uniqueness; stability; optimal control problem

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MDPI and ACS Style

Gissy, H.; Ahmadini, A.A.H.; Salahuddin. Solutions for the Nonlinear Mixed Variational Inequality Problem in the System. Symmetry 2024, 16, 796. https://doi.org/10.3390/sym16070796

AMA Style

Gissy H, Ahmadini AAH, Salahuddin. Solutions for the Nonlinear Mixed Variational Inequality Problem in the System. Symmetry. 2024; 16(7):796. https://doi.org/10.3390/sym16070796

Chicago/Turabian Style

Gissy, Husain, Abdullah Ali H. Ahmadini, and Salahuddin. 2024. "Solutions for the Nonlinear Mixed Variational Inequality Problem in the System" Symmetry 16, no. 7: 796. https://doi.org/10.3390/sym16070796

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