Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Solutions for the System of Nonlinear Mixed Variational Inequality Problems

Version 1 : Received: 17 April 2024 / Approved: 18 April 2024 / Online: 18 April 2024 (11:24:36 CEST)

A peer-reviewed article of this Preprint also exists.

Gissy, H.; Ahmadini, A.A.H.; Salahuddin. Solutions for the Nonlinear Mixed Variational Inequality Problem in the System. Symmetry 2024, 16, 796. Gissy, H.; Ahmadini, A.A.H.; Salahuddin. Solutions for the Nonlinear Mixed Variational Inequality Problem in the System. Symmetry 2024, 16, 796.

Abstract

In this paper, we propose a system of nonlinear mixed variational inequality problems, which consists of two elliptic mixed variational inequality problems on Banach spaces. Under suitable assumptions, using the Kakutani-Ky Fan fixed point theorem and Minty techniques, we prove the solution set to the system of nonlinear mixed variational inequality problem is nonempty, weakly compact and unique. Additionally, we suggest a stability result for the system of nonlinear mixed variational inequality problem by perturbing the duality mappings. Furthermore, we present an optimal control problem governed by the system of nonlinear mixed variational inequality problems and establish a solvability result.

Keywords

System of nonlinear mixed variational inequality problem; Inverse relaxed monotonicity; Existence; Stability

Subject

Computer Science and Mathematics, Applied Mathematics

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