Integration of multivalued operators and cyclic submonotonicity

Aris Daniilidis, Pando Georgiev, Jean Paul Penot

Research output: Contribution to journalArticleResearchpeer-review

16 Citations (Scopus)


We introduce a notion of cyclic submonotonicity for multivalued operators from a Banach space X to its dual. We show that if the Clarke subdifferential of a locally Lipschitz function is strictly submonotone on an open subset U of X, then it is also maximal cyclically submonotone on U, and, conversely, that every maximal cyclically submonotone operator on U is the Clarke subdifferential of a locally Lipschitz function, which is unique up to a constant if U is connected. In finite dimensions these functions are exactly the lower C1 functions considered by Spingarn and Rockafellar.
Original languageEnglish
Pages (from-to)177-195
JournalTransactions of the American Mathematical Society
Publication statusPublished - 1 Jan 2003


  • Integration
  • Subdifferential
  • Submonotone operator
  • Subsmooth function


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