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, Università di Bergamo, Via dei Caniana 2, 24127 Bergamo, Italy
marco.rocco@unibg.it
Juan Enrique Martínez-Legaz
Dep. d'Economia i d'Història Econòmica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
juanenrique.martinez.legaz@uab.cat
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.
Keywords: Monotone operator, type (D), convex representation, bidual, surjectivity, Fenchel duality.
MSC: 47H05, 46T99, 47N10
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