Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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
and: MOVE (Markets, Organizations and Votes in Economics)

juanenrique.martinez.legaz@uab.cat

Keywords

  • Monotone operator
  • type (D)
  • convex representation
  • bidual
  • surjectivity
  • Fenchel duality

Mathematics Subject Classification

47H05, 46T99, 47N10

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Suggested citation

M. Rocco, J. E. Martínez-Legaz. “On Surjectivity Results for Maximal Monotone Operators of Type (D).” Journal of Convex Analysis 18 (2011), No. 2, 545–576. https://doi.org/10.68381/jca18035

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Published by Heldermann Verlag, 2011. Rights now held by Banach Press LLC.