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Ubiquitous Subdifferentials, r L –density and Maximal Monotonicity

Abstract

In this paper, we first investigate an abstract subdifferential for which (using Ekeland’s variational principle) we can prove an analog of the Brøndsted–Rockafellar property. We introduce the “ r L –density” of a subset of the product of a Banach space with its dual. A closed r L –dense monotone set is maximally monotone, but we will also consider the case of nonmonotone closed r L –dense sets. As a special case of our results, we can prove Rockafellar’s result that the subdifferential of a proper convex lower semicontinuous function is maximally monotone.

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Author information

Correspondence to Stephen Simons.

Additional information

This paper is dedicated to Lionel Thibault, in recognition of his contribution to convex analysis and related fields

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Simons, S., Wang, X. Ubiquitous Subdifferentials, r L –density and Maximal Monotonicity. Set-Valued Var. Anal 23, 631–642 (2015). https://doi.org/10.1007/s11228-015-0326-7

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Keywords

  • Abstract subdifferential
  • Brøndsted–Rockafellar property
  • Multifunction
  • Monotonicity
  • Monotone polar
  • r L –density

Mathematics Subject Classification (2000)

  • Primary 49J52; Secondary 47H04
  • 47H05
  • 65K10