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Solutions for the System of Nonlinear Mixed Variational Inequality Problems
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: 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
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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