Solvability of the System of Extended Nonlinear Mixed Variational-Like Inequalities and Proximal Dynamical System

In this article, our goal is to study the system of extended nonlinear mixed variational-like inequalities (in short, SENMVLI) with a nonconvex functional in the setting of real Hilbert spaces and discuss the existence of solution of our considered problem. We propose a three-step iterative algorithm to calculate the approximate solutions of SENMVLI and investigate the convergence analysis as well as stability analysis of the proposed algorithm. Furthermore, we also study the proximal dynamical system for SENMVLI and prove that the trajectory of the solution of the extended proximal dynamical system converges globally exponentially to a unique solution of SENMVLI. Our suggested iterative algorithm and results have become the significant improvement, enhancement, and generalization of many previously known results in the literature.