H(·,·)-accretive operator with an application for solving variational inclusions in Banach spaces

In this paper, a new H(·,·)-accretive operator is introduced in Banach spaces and the Lipschitzian continuity of the resolvent operator for the H(·,·)-accretive operator is showed. By using the technique of resolvent operator, an iterative algorithm for solving a class of variational inclusions is constructed. Under some suitable conditions, the existence of the solution for the variational inclusions and the convergence of iterative sequence generated by the algorithm is proved. Some illustrative examples are also given.