STRONGLY NONLINEAR NONCONVEX VARIATIONAL INEQUALITIES

In this paper, we introduce and consider a new class of nonconvex variational inequalities involving two nonlinear operators, which is called the strongly nonlinear variational inequality. We establish the equivalence between the strongly nonlinear nonconvex variational inequalities and the fixed point problem. This alternative equivalence is used to study the existence of a solution of the strongly nonlinear nonconvex variational inequality and to suggest an iterative method. We consider the convergence criteria of the iterative method under suitable conditions. Some special cases are also discussed.