The existence of solutions for systems of generalized set-valued nonlinear quasi-variational inequalities

In this paper, we introduce and study a class of new systems of generalized set-valued nonlinear quasi-variational inequalities in a Hilbert space. By using the projection operator technique and the system of Wiener-Hopf equations technique, we suggest several new iterative algorithms to find the approximate solutions to these problems and prove the convergence of the different types of iterative sequences respectively. It is the first time that the system of Wiener-Hopf equations technique has been used to solve the system of variational inequalities problems, and the technique is more general than the projection operator technique. Our results improve and extend some known results in the literature.