Abstract
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 language | English |
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Pages (from-to) | 2071-2087 |
Number of pages | 17 |
Journal | Optimization |
Volume | 68 |
Issue number | 11 |
DOIs | |
State | Published - 2 Nov 2019 |
Bibliographical note
Publisher Copyright:© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.
Keywords
- 47H04
- 47H05
- 49J53
- Brézis–Browder theorem
- Fitzpatrick functions of order p
- linear p-cyclically monotone operators
- p-cyclically monotone operators