Geodesic
Separation by Convex Interpolation Families
Journal of convex analysis, Tome 20 (2013) no. 4, pp. 937-946.

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

A set of continuous functions defined on an interval I is called an n-parameter Beckenbach family, if each n points of I × R (with pairwise distinct first coordinates) can be interpolated by a unique element of the set. The aim of the present note is to characterize such pairs of real valued functions that can be separated by a member of a given convex Beckenbach family of order n. The key idea of the proof is to identify the family with Rn via a suitable homeomorphism. Then, the classical Helly Theorem guarantees the existence of a proper separator.
Classification : 26A51, 39B62, 52A20
Mots-clés : Interpolation families, Haar and Chebyshev systems, Separation theorems, Helly's Theorem 
@article{JCA_2013_20_4_JCA_2013_20_4_a2,
     author = {M. Bessenyei and P. Szokol},
     title = {Separation by {Convex} {Interpolation} {Families}},
     journal = {Journal of convex analysis},
     pages = {937--946},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2013},
     url = {http://geodesic.mathdoc.fr/item/JCA_2013_20_4_JCA_2013_20_4_a2/}
}
TY  - JOUR
AU  - M. Bessenyei
AU  - P. Szokol
TI  - Separation by Convex Interpolation Families
JO  - Journal of convex analysis
PY  - 2013
SP  - 937
EP  - 946
VL  - 20
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JCA_2013_20_4_JCA_2013_20_4_a2/
ID  - JCA_2013_20_4_JCA_2013_20_4_a2
ER  - 
%0 Journal Article
%A M. Bessenyei
%A P. Szokol
%T Separation by Convex Interpolation Families
%J Journal of convex analysis
%D 2013
%P 937-946
%V 20
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JCA_2013_20_4_JCA_2013_20_4_a2/
%F JCA_2013_20_4_JCA_2013_20_4_a2
M. Bessenyei; P. Szokol. Separation by Convex Interpolation Families. Journal of convex analysis, Tome 20 (2013) no. 4, pp. 937-946. http://geodesic.mathdoc.fr/item/JCA_2013_20_4_JCA_2013_20_4_a2/