Remarks on p-cyclically monotone operators

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In this paper, we deal with three aspects of p-cyclically monotone operators. First, we introduce a notion of monotone polar adapted for p-cyclically monotone operators and study these kinds of operators with a unique maximal extension (called pre-maximal), and with a convex graph. We then deal with linear operators and provide characterizations of p-cyclical monotonicity and maximal p-cyclical monotonicity. Finally, we show that the Brézis-Browder theorem preserves p-cyclical monotonicity in reflexive Banach spaces.
Original languageEnglish
Pages (from-to)2071-2087
Number of pages17
Issue number11
StatePublished - 2 Nov 2019

Bibliographical note

Publisher Copyright:
© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.


  • 47H04
  • 47H05
  • 49J53
  • Brézis–Browder theorem
  • Fitzpatrick functions of order p
  • linear p-cyclically monotone operators
  • p-cyclically monotone operators


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