we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}, $h$-...

In this work we are concerned with maximality of monotone operators representable by certain convex functions in non-reflexive Banach spaces. We also prove that these maximal monotone operators satisfy a Brønsted-Rockafellar type property. 2000 Mathematics Subject Classification: 47H05, 49J52, 47N10.

We show a surprising connexion between a property of the inf convolutions of a family of convex lower semicontinuous functions and the fact that intersections of maximal cyclically monotone graphs are the critical set of a bipotential. We then extend the results from [4] to bipotentials convex covers, generalizing the notion of a bi-implicitly convex lagrangian cover. As an application we prove...

MOTIVATION Given a large-scale biological network represented as an influence graph, in this article we investigate possible decompositions of the network aimed at highlighting specific dynamical properties. RESULTS The first decomposition we study consists in finding a maximal directed acyclic subgraph of the network, which dynamically corresponds to searching for a maximal open-loop subsyst...

This paper has been motivated by general considerations on the topic of Risk Measures, which essentially are convex monotone maps de…ned on spaces of random variables, possibly with the so-called Fatou property. We show …rst that the celebrated Namioka-Klee theorem for linear, positive functionals holds also for convex monotone maps on Frechet lattices. It is well-known among the specialists th...