\(H(\cdot ,\cdot)\)-cocoercive operator and an application for solving generalized variational inclusions (Q638111)

Summary: The purpose of this paper is to introduce a new \(H(\cdot, \cdot)\)-cocoercive operator, which generalizes many existing monotone operators. The resolvent operator associated with the \(H(\cdot ,\cdot)\)-cocoercive operator is defined, and its Lipschitz continuity is proved. 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.