The Dynamical System for System of Variational Inequality Problem in Hilbert Spaces - Petrot, Narin; Tangkhawiwetkul, Jittiporn (Communications in Mathematics and Applications, 2018)
In this paper, we will present a dynamical system which relates to the system of variational inequality problem by starting with introducing a Wiener-Hopf equation for the system of variational inequality problem and using a such Wiener-Hopf equation for proposing a dynamical system for the system of variational inequality problem. Moreover, the existence solution of such dynamical system is considered and the stability, globally asymptotically stable and also globally exponential convergence, of the solution for the system of a such dynamical system are proved. The results in this paper improve and extend the variational inequality problems which have been appeared in literature.
Keywords: Dynamical system; The system of variational inequality; Lipschitz mapping; Lyapunov's stability theorem; Gronwall's Lemma