NONCONVEX QUASI VARIATIONAL INEQUALITIES

In this paper, we introduce and consider a new class of quasi variational inequalities, which is called the nonconvex quasi variational inequality. We show that the projection method can be used to establish the equivalence between the nonconvex quasi variational inequalities and the fixed points problems and the Wiener-Hopf equations. We use this equivalent alternative formulation to suggest and analyze a new class of two-step iterative methods for solving the nonconvex variational inequalities. We discuss the convergence of the iterative method under suitable conditions conditions. Our method of proofs is very simple as compared with other techniques.