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H-monotone operator and resolvent operator technique for variational inclusions. (English) Zbl 1030.49008
Summary: 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.

MSC:
49J40Variational methods including variational inequalities