Generalized multivalued quasi-variational inequalities

In this paper, we introduce and study a new class of variational inequalities, known as generalized multivalued quasi-variational inequalities. This class is the most general and unifying one. Using essentially the projection technique, we establish the equivalence between this class and the implicit Wiener-Hopf equations. This equivalence is used to suggest a number of iterative algorithms for solving the generalized multivalued quasi-variational inequalities. The convergence analysis of these algorithms is also studied. The results proved in this paper represent a significant improvement and refinement of the previously known results in this area.