On the convergence of iterative method for solving a variational inequality of the second kind with inversely strongly monotone operator

In the paper the convergence of the iterative method for solving a variational inequality of the second kind with inversely strongly monotone operator in Hilbert space is investigated. The functional occurring in this variational inequality is a sum of several functionals. Each of these functionals is a superposition of lower semi-continuous convex proper functional and a linear continuous operator. Such variational inequalities arise, in particular, during mathematical modeling of stationary problems of filtration of a non-compressible fluid follows the nonlinear multi-valued anisotropic filtration law with limiting gradient.