
Journal of Convex Analysis 19 (2012), No. 1, 171183 Copyright Heldermann Verlag 2012 On Plis Metric on the Space of Strictly Convex Compacta Maxim Viktorovich Balashov Dept. of Higher Mathematics, Moscow Institute of Physics and Technology, Institutski str. 9, Dolgoprudny, Moscow Region, Russia 141700 balashov@mail.mipt.ru Dusan Repovs Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia dusan.repovs@guest.arnes.si We consider a certain metric on the space of all convex compacta in R^{n}, introduced by A. Plis ["Uniqueness of optimal trajectories for nonlinear control problems, Ann. Polon. Math. 29 (1975), 397401]. The set of strictly convex compacta is a complete metric subspace of the metric space of convex compacta with respect to this metric. We present some applications of this metric to the problems of setvalued analysis, in particular we estimate the distance between two compact sets with respect to this metric and to the Hausdorff metric. Keywords: Metric space, strictly convex compactum, modulus of convexity, setvalued mapping, strict convexity, uniform convexity, supporting function, Demyanov distance, Hausdorff distance. MSC: 54A20, 52A41; 52A20, 52A99, 46N10 [ Fulltextpdf (157 KB)] for subscribers only. 