ITERATIVE APPROXIMATION FOR A NEW SYSTEM OF GENERAL NONLINEAR SET-VALUED VARIATIONAL INCLUSIONS WITH (H,eta)-MONOTONE MAPPINGS

Abstract

In this paper, we introduce and study a new system of general nonlinear set-valued variational inclusions involving (H,eta)-monotone mappings in Hilbert spaces. By using the resolvent operator associated with (H,eta)-monotone mapping due to Fang, Huang and Thompson, we construct some new iterative algorithms for approximating the solutions of this new system of variational inclusions. We also prove the existence of solutions and the convergence of the sequences generated by the algorithm in Hilbert spaces. The results presented in this paper generalize, improve, and unify some recent results in this field.