A new system of variational inclusions involving H(·,·)-accretive operator in Banach spaces

In this paper, we introduced and study a new class of system of variational inclusions involving H(·,·)-accretive operator in Banach spaces. By using the resolvent operator technique associated with H(·,·)-accretive operator, we prove the existence of the solution for the system of inclusions and develop a step-controlled iterative algorithm to approach the unique solution.