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Acta Mathematica Vietnamica

ON THE MAXIMAL MONOTONICITY OF SUBDIFFERENTIALS

icon-email DINH THE LUC

Abstract

We prove that a lower semicontinuous function from a Banach space to the extended real line is convex if and only if its subdifferential is monotone. A simple proof of the maximality of monotone subdifferentials is also given.

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Viện Hàn lâm Khoa học và Công nghệ Việt Nam Hội Toán học Việt Nam Viện Nghiên cứu Cao cấp về toán MathScinet Arxiv