H(⋅,⋅)-Cocoercive Operator and an Application for Solving Generalized Variational Inclusions

Abstract

The purpose of this paper is to introduce a new H(⋅,⋅)-cocoercive operator, which generalizes many existing monotone operators. The resolvent operator associated with H(⋅,⋅)-cocoercive operator is defined, and its Lipschitz continuity is presented. By using techniques of resolvent operator, a new iterative algorithm for solving generalized variational inclusions is constructed. Under some suitable conditions, we prove the convergence of iterative sequences generated by the algorithm. For illustration, some examples are given.