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Journal of Convex Analysis 18 (2011), No. 2, 545--576
Copyright Heldermann Verlag 2011

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

Marco Rocco
Dip. di Matematica, UniversitÓ di Bergamo, Via dei Caniana 2, 24127 Bergamo, Italy

Juan Enrique MartÝnez-Legaz
Dep. d'Economia i d'Hist˛ria Econ˛mica, Universitat Aut˛noma de Barcelona, 08193 Bellaterra, Spain

A generalization of Rockafellar's surjectivity theorem was provided by J.E. MartÝnez-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.

Keywords: Monotone operator, type (D), convex representation, bidual, surjectivity, Fenchel duality.

MSC: 47H05, 46T99, 47N10

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