Iterative methods for solving a system of variational inclusions involving H–ηH–η-monotone operators in Banach spaces

In this paper, we introduce and study a new system of variational inclusions involving H–ηH–η-monotone operators in Banach space. Using the resolvent operator associated with H–ηH–η-monotone operators, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm.