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In this paper, we deal with three aspects of p-monotone operators. First we study p-monotone operators with a unique maximal extension (called pre-maximal), and with convex graph. We then deal with linear operators, and provide characterizations of p-monotonicity and maximal p-monotonicity. Finally we show that the Brezis-Browder theorem preserves p-monotonicity in reflexive Banach spaces.

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