New general systems of set-valued variational inclusions involving relative (A,η)-maximal monotone operators in Hilbert spaces

The purpose of this paper is to introduce and study a class of new general systems of set-valued variational inclusions involving relative (A,η)-maximal monotone operators in Hilbert spaces. By using the generalized resolvent operator technique associated with relative (A,η)-maximal monotone operators, we also construct some new iterative algorithms for finding approximation solutions to the general systems of set-valued variational inclusions and prove the convergence of the sequences generated by the algorithms. The results presented in this paper improve and extend some known results in the literature.