Remarks on p-cyclically monotone operators. (2nd November 2019) - Bueno, Orestes; Cotrina, John
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.