An Additive Subfamily of Enlargements of a Maximally Monotone Operator

© 2015, Springer Science+Business Media Dordrecht. We introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These enlargements constitute a subfamily of the family of enlargements introduced by Svaiter. When the operator under consideration is the subdifferential of a convex lower semicontinuous proper function, we prove that some members of the subfamily are smaller than the classical ε-subdifferential enlargement widely used in convex analysis. We also recover the ε-subdifferential within the subfamily. Since they are all additive, the enlargements in our subfamily can be seen as structurally closer to the ε-subdifferential enlargement.