H-Monotone operator and resolvent operator technique for variational inclusions

摘要

In this paper, we introduce a new class of monotone operators––H-monotone operators. The resolvent operator associated with an H-monotone operator is defined and its Lipschitz continuity is presented. We also introduce and study a new class of variational inclusions involving H-monotone operators and construct a new algorithm for solving this class of variational inclusions by using the resolvent operator technique.