Gissy, H.; Ahmadini, A.A.H.; Salahuddin. Solutions for the Nonlinear Mixed Variational Inequality Problem in the System. Symmetry2024, 16, 796.
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. Symmetry2024, 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:
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