Remarks on p-cyclically monotone operators

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.

KEYWORDS:

• p-cyclically monotone operators
• Fitzpatrick functions of order p
• linear p-cyclically monotone operators
• Brézis–Browder theorem

AMS SUBJECT CLASSIFICATIONS:

• 47H04
• 47H05
• 49J53

Acknowledgements

We would like to thank the anonymous referees for the suggestions and comments, which helped to improve this work.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Orestes Bueno  http://orcid.org/0000-0002-7950-2876

John Cotrina  http://orcid.org/0000-0001-5034-6286

Additional information

Funding

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.