Narrow Results

In this paper, we introduce a new class of nonlinear variational inclusions with H-monotone mappings. By using the resolvent operator method associated with H-monotone mappings in Hilbert spaces, we prove the existence and uniqueness of solution for this class of nonlinear variational inclusions. We also construct a new Ishikawa type iterative algorithm for finding approximate the solution of this nonlinear variational inclusion and discuss the convergence and stability of sequence of iterates generated by the algorithm. The present results improve and extend many known results in the literature.

In this paper, we introduce and study a new system of set-valued variational inclusions involving H-monotone mappings in Hilbert spaces. By using the resolvent operator method associated with H-monotone mappings, we construct a new iterative algorithm approximating the solution of this system of set-valued variational inclusion and discuss the convergence analysis of the algorithm.