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Journal of Convex Analysis 18 (2011), No. 3, 865--872
Copyright Heldermann Verlag 2011

Moderation of Convex Bodies

Jin-ichi Itoh
Faculty of Education, Kumamoto University, Kumamoto 860-8555, Japan

Tudor Zamfirescu
Institute of Mathematics, Roumanian Academy of Sciences, P.O.B. 1-764, Buchrest 014700, Roumania

Everybody knows what an extreme point of a convex body is. Does this notion have an opposite? A most non-extreme point? Or: can we somehow say that a point is more or less extreme than another? In this paper we show a way to do this. We shall define the notion of moderation for points of a convex body. Then the points of largest moderation will be the moderate, those of smallest moderation the extreme points, as you would expect.

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