Existence of Solutions to the System of Generalized Implicit Vector Quasivariational Inequality Problems

Abstract

We study the system of generalized implicit vector quasivariational inequality problems and prove a new existence result of its solutions by Kakutani-Fan-Glicksberg's fixed points theorem. As a special case, we also derive a new existence result of solutions to the generalized implicit vector quasivariational inequality problems.

The existence and stability of solutions for symmetric generalized quasi-variational inclusion problems

“…In recent years, a lot of results for existence of solutions and stability of solutions for symmetric vector quasiequilibrium problems, vector quasi-equilibrium problems, vector quasi-variational inequality problems and optimization problems have been established by many authors in different ways. For example, equilibrium problems [1-10, 15-17, 19, 23-25, 29, 34, 35, 37, 40, 41], variational inequality problems [25,30,31,36,42,43], optimization problems [35,42,43], variational relation problems [12,13,27,28,32,33] and the references therein.…”