
Journal of Convex Analysis 18 (2011), No. 3, 865872 Copyright Heldermann Verlag 2011 Moderation of Convex Bodies Jinichi Itoh Faculty of Education, Kumamoto University, Kumamoto 8608555, Japan jitoh@gpo.kumamotou.ac.jp Tudor Zamfirescu Institute of Mathematics, Roumanian Academy of Sciences, P.O.B. 1764, Buchrest 014700, Roumania tudor.zamfirescu@mathematik.unidortmund.de Everybody knows what an extreme point of a convex body is. Does this notion have an opposite? A most nonextreme 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. [ Fulltextpdf (116 KB)] for subscribers only. 