On the iterative method for solving a variational inequalities with inversely strongly monotone operators

We consider a boundary valued problem whose generalized statement is formulated as a mixed variational inequality in Hilbert space. The operator of this variational inequality is a sum of several inversely strongly monotone operators (which are not necessarily potential operators). The functional occurring in this variational inequality is also a sum of several lower semi-continuous convex proper functionals. For the solving of the considered variational inequality the decomposition iterative method is offered. The suggested method does not require the inversion of original operators. The convergence of this method is investigated.