Geodesic
On Plis Metric on the Space of Strictly Convex Compacta
Journal of convex analysis, Tome 19 (2012) no. 1, pp. 171-183 Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

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 
@article{JCA_2012_19_1_JCA_2012_19_1_a9,
     author = {M. V. Balashov and D. Repovs},
     title = {On {Plis} {Metric} on the {Space} of {Strictly} {Convex} {Compacta}},
     journal = {Journal of convex analysis},
     pages = {171--183},
     year = {2012},
     volume = {19},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2012_19_1_JCA_2012_19_1_a9/}
}
TY  - JOUR
AU  - M. V. Balashov
AU  - D. Repovs
TI  - On Plis Metric on the Space of Strictly Convex Compacta
JO  - Journal of convex analysis
PY  - 2012
SP  - 171
EP  - 183
VL  - 19
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JCA_2012_19_1_JCA_2012_19_1_a9/
ID  - JCA_2012_19_1_JCA_2012_19_1_a9
ER  - 
%0 Journal Article
%A M. V. Balashov
%A D. Repovs
%T On Plis Metric on the Space of Strictly Convex Compacta
%J Journal of convex analysis
%D 2012
%P 171-183
%V 19
%N 1
%U http://geodesic.mathdoc.fr/item/JCA_2012_19_1_JCA_2012_19_1_a9/
%F JCA_2012_19_1_JCA_2012_19_1_a9
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/