System of implicit nonconvex variationl inequality problems A projection method approach

In this paper, we consider a new system of implicit nonconvex variational inequality problems in setting of prox-regular subsets of two different Hilbert spaces. Using projection method, we establish the equivalence between the system of implicit nonconvex variational inequality problems and a system of relations. Using this equivalence formulation, we suggest some iterative algorithms for finding the approximate solution of the system of implicit nonconvex variational inequality problems and its special case. Further, we establish some theorems for the existence and iterative approximation of the solutions of the system of implicit nonconvex variational inequality problems and its special case. The results presented in this paper are new and different form the previously known results for nonconvex variational inequality problems. These results also generalize, unify and improve the previously known results of this area.