A Unified Approach to Extended General Quasi Variational Inclusions

In this article, we introduce and consider some new classes of extended general quasi variational inclusions, which provide us with a unified, natural and simple framework to consider a wide class of unrelated problems arising in pure and applied sciences. We establish the equivalence between the general quasi variational inclusions and the fixed point problems. This alternative equivalence formulation is applied to discuss the existence of a solution as well as to propose some iterative methods. Convergence analysis is investigated under certain mild conditions. We introduce a new class of dynamical systems associated with extended general quasi variational inclusions. We have used the dynamical systems to suggest and analyzed some implicit iterative methods for solving the extended general quasi variational inclusions. Since the extended general quasi variational inclusions include quasi variational inclusions, absolute vale equations, complementarity problems, variational inequalities, and related optimization problems as special cases, our results continue to hold for these problems. It is an interesting problem to compare these methods with other technique for solving quasi variational inclusions for further research activities.