A proximal neurodynamic model for a system of non-linear inverse mixed variational inequalities

Anjali Upadhyay; Rahul Pandey

doi:10.1016/j.neunet.2024.106323

A proximal neurodynamic model for a system of non-linear inverse mixed variational inequalities

Neural Netw. 2024 Apr 15:176:106323. doi: 10.1016/j.neunet.2024.106323. Online ahead of print.

Authors

Anjali Upadhyay¹, Rahul Pandey²

Affiliations

¹ Department of Mathematics, University of Delhi, Delhi, India. Electronic address: aubhudu@gmail.com.
² Mahant Avaidyanath Govt. Degree College, Jungle Kaudiya, Gorakhpur, U.P., India. Electronic address: rahulmangdc@gmail.com.

PMID: 38653123
DOI: 10.1016/j.neunet.2024.106323

Abstract

In this article, we introduce a system of non-linear inverse mixed variational inequalities (SNIMVIs). We propose a proximal neurodynamic model (PNDM) for solving SNIMVIs, leveraging proximal mappings. The uniqueness of the continuous solution for the PNDM is proved by assuming Lipschitz continuity. Moreover, we establish the global asymptotic stability of equilibrium points of the PNDM, contingent upon Lipschitz continuity and strong monotonicity. Additionally, an iterative algorithm involving proximal mappings for solving the SNIMVIs is presented. Finally, we provide illustrative examples to support our main findings. Furthermore, we provide an example where the SNIMVIs violate the strong monotonicity condition and exhibit the divergence nature of the trajectories of the corresponding PNDM.

Keywords: Fixed point; Inverse mixed variational inequalities; Lipschitz continuity; Lyapunov stability; Proximal neurodynamic model; Strong monotonicity.