Remarks on <i>p</i>-cyclically monotone operators

In this paper, we deal with three aspects of <i>p</i>-cyclically monotone operators. First, we introduce a notion of monotone polar adapted for <i>p</i>-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 <i>p</i>-cyclical monotonicity and maximal <i>p</i>-cyclical monotonicity. Finally, we show that the Brézis-Browder theorem preserves <i>p</i>-cyclical monotonicity in reflexive Banach spaces.