ITERATIVE SCHEMES FOR SOLVING GENERAL VARIATIONAL INEQUALITIES

In this paper, we consider a new class of variational inequalities involving two operators, which is called the general variational inequality. We have shown that the general variational inequalities are equivalent to the fixed point problem using the projection technique. This equivalent fixed point formulation is used to discuss the existence of solution as well as to investigate several iterative methods for solving general variational inequalities. Some applications of the associated dynamical system coupled with finite difference are explored. Convergence analysis of the proposed methods is considered under suitable conditions. Since general variational inequalities include the variational inequalities, complementarity problems and nonlinear equations as special cases, our results continued to hold for these problems. The techniques and ideas of this paper be starting point for the future research.