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.
Nota bibliográficaFunding Information:
This research was partially supported by Consejo Nacional de Ciencia, Tecnología e Innovación Tecnológica, Cienciactiva - CONCYTEC EE020-MATH Amsud Project No. 003-2017 and by Math Amsud 17-MATH-06. We would like to thank the anonymous referees for the suggestions and comments, which helped to improve this work.
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- Brézis–Browder theorem
- Fitzpatrick functions of order p
- linear p-cyclically monotone operators
- p-cyclically monotone operators