Geodesic
On Surjectivity Results for Maximal Monotone Operators of Type (D)
Journal of convex analysis, Tome 18 (2011) no. 2, pp. 545-576

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 47H05, 46T99, 47N10
Mots-clés : Monotone operator, type (D), convex representation, bidual, surjectivity, Fenchel duality 
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     author = {M. Rocco and J. E. Mart{\'\i}nez-Legaz},
     title = {On {Surjectivity} {Results} for {Maximal} {Monotone} {Operators} of {Type} {(D)}},
     journal = {Journal of convex analysis},
     pages = {545--576},
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     volume = {18},
     number = {2},
     year = {2011},
     url = {http://geodesic.mathdoc.fr/item/JCA_2011_18_2_JCA_2011_18_2_a18/}
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M. Rocco; J. E. Martínez-Legaz. On Surjectivity Results for Maximal Monotone Operators of Type (D). Journal of convex analysis, Tome 18 (2011) no. 2, pp. 545-576. http://geodesic.mathdoc.fr/item/JCA_2011_18_2_JCA_2011_18_2_a18/