by  Andrei Verona & Maria E. Verona

We study monotone operators on quasi open or convex subsets of a real Banach space X (quasi open means that the contingent cone at each point equals X). Among others we characterize the maximality of such an operator in terms of its upper semicontinuity properties and, in the case of a convex domain, also in terms of its behaviour at the support points. We next give sufficient conditions for such an operator to be generically single valued, extending Kenderov's theorems. As an application we reobtain generic Gateaux and Frechet differentiability results for convex functions defined on not necessarily open convex sets.