Geodesic
On Plis Metric on the Space of Strictly Convex Compacta
Journal of convex analysis, Tome 19 (2012) no. 1, pp. 171-183.

Voir la notice de l'article provenant de la source Heldermann Verlag

We consider a certain metric on the space of all convex compacta in Rn, introduced by A. Plis ["Uniqueness of optimal trajectories for non-linear control problems, Ann. Polon. Math. 29 (1975), 397-401]. 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 set-valued analysis, in particular we estimate the distance between two compact sets with respect to this metric and to the Hausdorff metric.
Classification : 54A20, 52A41, 52A20, 52A99, 46N10
Mots-clés : Metric space, strictly convex compactum, modulus of convexity, set-valued mapping, strict convexity, uniform convexity, supporting function, Demyanov distance, Hausdorff distance 
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     title = {On {Plis} {Metric} on the {Space} of {Strictly} {Convex} {Compacta}},
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M. V. Balashov; D. Repovs. On Plis Metric on the Space of Strictly Convex Compacta. Journal of convex analysis, Tome 19 (2012) no. 1, pp. 171-183. http://geodesic.mathdoc.fr/item/JCA_2012_19_1_JCA_2012_19_1_a9/