Graph convergence for H(., .)-cocoercive operator in q-uniformly smooth Banach spaces with an application

Abstract

In this paper, we consider a class of H(., .) -cocoercive operator, which generalizes many existing monotone operators. Further, we introduce a concept of graph convergence concerned with the H(., .)-cocoercive operator in q-uniformly smooth Banach spaces and given an equivalence theorem between graph-convergence and resolvent operator convergence for the H(., .)-cocoercive operator. As an application, a perturbed algorithm for solving a class of variational inclusion involving H(., .)-cocoercive operator is constructed. Furthermore, under some suitable conditions, the existence of the solution for the variational inclusion and the convergence of iterative sequence generated by perturbed algorithm are given.