Abstract

We give some properties of the Rockafellar function used in integration theory of cyclically monotone mappings. This function is proper only in the case of cyclically monotone mappings. But, by a slight modification of its definition we can obtain a proper function even if the mapping is not cyclically monotone. Finally, two dual properties are established.

Author information

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

Teodor Precupanu

Dept. of Mathematics, University "Al. I. Cuza", Bd. Carol 11, 700506 Iasi, Romania

tprecup@uaic.ro

Keywords

  • Rockafellar function
  • cyclically monotone mapping
  • support function
  • subdifferential
  • Darboux integral
  • conjugate function

Mathematics Subject Classification

47H05, 52A41, 46B20

Suggested citation

T. Precupanu. “On the Rockafellar Function Associated to a Cyclically Monotone Mapping.” Journal of Convex Analysis 24 (2017), No. 1, 319–331. https://doi.org/10.68381/jca24022

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Published by Heldermann Verlag, 2017. Rights now held by Banach Press.