On Surjectivity Results for Maximal Monotone Operators of Type (D)

A generalization of Rockafellar's surjectivity theorem was provided by J.E. Martínez-Legaz in a recent article ["Some generalizations of Rockafellar's surjectivity theorem", Pac. J. Optim. 4 (2008) 527-548], replacing the duality mapping by any maximal monotone operator having finite-valued Fitzpatrick function. The present paper extends this result to the nonreflexive setting for maximal monotone operators of type (D) and refines the finite-valuedness condition on the Fitzpatrick function. Moreover, a characterization of surjectivity properties for the sum of two maximal monotone operators of type (D) in terms of Fenchel duality is given.