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Any finite, separately convex, positively homogeneous function on R is convex. This was first established in [1]. In this paper, we give a new and concise proof of this result, and we show that it fails in higher dimension. The key of the new proof is the notion of perspective of a convex function f , namely, the function (x, y) → yf(x/y), y > 0. In recent works [9, 10, 11], the perspective has...
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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 1988
ISSN: 0294-1449
DOI: 10.1016/s0294-1449(16)30351-1