Graph convergence for the H(·, ·)-accretive operator in Banach spaces with an application

In this paper, a concept of graph convergence concerned with the H(·, ·)-accretive operator is introduced in Banach spaces and some equivalence theorems between of graph-convergence and resolvent operator convergence for the H(·, ·)-accretive operator sequence are proved. As an application, a perturbed algorithm for solving a class of variational inclusions involving the H(·, ·)-accretive operator is constructed. Under some suitable conditions, the existence of the solution for the variational inclusions and the convergence of iterative sequence generated by the perturbed algorithm are also given.