Remarks on p-cyclically monotone operators. (2nd November 2019)

• Record Type: Journal Article
• Authors: Bueno, Orestes; Cotrina, John
• Is Part Of: Optimization. Volume 68:Number 11(2019)
• Page Start: 2071
• Page End: 2087
• Publication Date: 2019-11-02
• Subjects: p-cyclically monotone operators -- Fitzpatrick functions of order p -- linear p-cyclically monotone operators -- Brézis–Browder theorem; 47H04 -- 47H05 -- 49J53; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1636049
• Languages: English
• ISSNs: 0233-1934

Abstract

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.