\(\varepsilon\)-enlargements of maximal monotone operators in Banach spaces (Q1819204)

Given a maximal monotone operator \(T\) in a Banach space, we consider an enlargement \(T^\varepsilon\), in which monotonicity is lost up to \(\varepsilon\), in a very similar way to the \(\varepsilon\)-subdifferential of a convex function. We establish in this general framework some theoretical properties of \(T^\varepsilon\), like a transportation formula, local Lipschitz continuity, local boundedness, and a Brøndsted-Rockafellar property.