Geodesic
Weak Concavity of the Antidistance Function
Journal of convex analysis, Tome 21 (2014) no. 4, pp. 951-964.

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

We prove that the function which for a given point of a Banach space gives the largest distance to the points of a given convex closed bounded set (antidistance) is weakly concave on the complement to some neighborhood of the set if and only if the set is a summand of some ball of some radius. We obtain precise estimates for parameters of weak concavity via the size of the neighborhood and radius of the ball in the Hilbert space.
Classification : 49J52, 58C20, 52A07, 26B25, 52A41, 52A05
Mots-clés : Antidistance function, uniform convexity, uniform smoothness, weak concavity, modulus of weak concavity, proximal smoothness, P-supporting condition 
@article{JCA_2014_21_4_JCA_2014_21_4_a2,
     author = {M. V. Balashov and M. O. Golubev},
     title = {Weak {Concavity} of the {Antidistance} {Function}},
     journal = {Journal of convex analysis},
     pages = {951--964},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {2014},
     url = {http://geodesic.mathdoc.fr/item/JCA_2014_21_4_JCA_2014_21_4_a2/}
}
TY  - JOUR
AU  - M. V. Balashov
AU  - M. O. Golubev
TI  - Weak Concavity of the Antidistance Function
JO  - Journal of convex analysis
PY  - 2014
SP  - 951
EP  - 964
VL  - 21
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JCA_2014_21_4_JCA_2014_21_4_a2/
ID  - JCA_2014_21_4_JCA_2014_21_4_a2
ER  - 
%0 Journal Article
%A M. V. Balashov
%A M. O. Golubev
%T Weak Concavity of the Antidistance Function
%J Journal of convex analysis
%D 2014
%P 951-964
%V 21
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JCA_2014_21_4_JCA_2014_21_4_a2/
%F JCA_2014_21_4_JCA_2014_21_4_a2
M. V. Balashov; M. O. Golubev. Weak Concavity of the Antidistance Function. Journal of convex analysis, Tome 21 (2014) no. 4, pp. 951-964. http://geodesic.mathdoc.fr/item/JCA_2014_21_4_JCA_2014_21_4_a2/