Abstract

In this paper, we introduce a new class of monotone operators ? (H(·, ·), ?)- monotone operators, which generalize many
existing monotone operators. The resolvent operator associated with an (H(·, ·), ?)- monotone operator is defined and
its Lipschitz continuity is presented. As an application, we also consider a new generalized mixed variational inclusion
involving (H(·, ·), ?)-monotone operators and construct a new algorithm for solving the generalized mixed variational inclusion.
Under some suitable conditions, we prove the convergence of the iterative sequences generated by the algorithm.
These results improve and generalize many corresponding results in recently literatures.

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