Solutions for the System of Nonlinear Mixed Variational Inequality Problems

H. Gissy; A. A. H. Ahmadini; Salahuddin .

doi:10.20944/preprints202404.1225.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

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.

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

Computer Science and Mathematics, Applied Mathematics

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Solutions for the System of Nonlinear Mixed Variational Inequality Problems

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