We consider whether the “inequality-splitting” property established in the Brøndsted– Rockafellar theorem for the subdifferential of a proper convex lower semicontinuous function on a Banach space has an analog for arbitrary maximal monotone multifunctions. We introduce the maximal monotone multifunctions of type (ED), for which an “inequality-splitting” property does hold. These multifunctions...

In this paper, we introduce a new class of monotone operators − (H(·, ·), η)monotone operators, which generalize many existing monotone operators. The resolvent operator associated with an (H(·, ·), η)monotone operator is defined and its Lipschitz continuity is presented. As an application, we also consider a new generalized mixed variational inclusion involving (H(·, ·), η)-monotone operators ...

In this paper, we investigate a fully nonlinear evolutionary Hamilton–Jacobi–Bellman (HJB) parabolic equation utilizing the monotone operator technique. We consider HJB arising from portfolio optimization selection, where goal is to maximize conditional expected value of terminal utility portfolio. The transformed into quasilinear using so-called Riccati transformation method. can be viewed as ...

We consider a generalized proximal point method for solving variational inequalities with maximal monotone operators in a Hilbert space. It proves to be that the conditions on the choice of a non-quadratic distance functional depend on the geometrical properties of the operator in the variational inequality, and – in particular – a standard assumption on the strict convexity of the kernel of th...