Geodesic
Generous Sets
Journal of convex analysis, Tome 28 (2021) no. 4, pp. 1265-128
Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

\def\Rk{{\mathbb{R}^k}} We investigate the notion of generosity, a particular case of non-selfishness. Let $\cal F$ be a family of sets in $\Rk$. A set $M \subset \Rk$ is called $\cal F$-{\it convex} if for any points $x,y\in M$ there is a set $F\in \cal F$ such that $x,y\in F$ and $F\subset M$. We call a family $\cal F$ of compact sets {\it complete} if $\cal F$ contains all compact $\cal F$-convex sets. A single convex body $K$ will be called {\it generous}, if the family of all convex bodies isometric to $K$ is not complete. We investigate here the generosity of convex bodies.
Classification : 52A10, 52A20
Mots-clés : F-convex, complete, generous, grateful 
@article{JCA_2021_28_4_JCA_2021_28_4_a15,
     author = {A. Fruchard and L. Yuan and T. Zamfirescu},
     title = {Generous {Sets}},
     journal = {Journal of convex analysis},
     pages = {1265--128},
     year = {2021},
     volume = {28},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2021_28_4_JCA_2021_28_4_a15/}
}
TY  - JOUR
AU  - A. Fruchard
AU  - L. Yuan
AU  - T. Zamfirescu
TI  - Generous Sets
JO  - Journal of convex analysis
PY  - 2021
SP  - 1265
EP  - 128
VL  - 28
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/JCA_2021_28_4_JCA_2021_28_4_a15/
ID  - JCA_2021_28_4_JCA_2021_28_4_a15
ER  - 
%0 Journal Article
%A A. Fruchard
%A L. Yuan
%A T. Zamfirescu
%T Generous Sets
%J Journal of convex analysis
%D 2021
%P 1265-128
%V 28
%N 4
%U http://geodesic.mathdoc.fr/item/JCA_2021_28_4_JCA_2021_28_4_a15/
%F JCA_2021_28_4_JCA_2021_28_4_a15
A. Fruchard; L. Yuan; T. Zamfirescu. Generous Sets. Journal of convex analysis, Tome 28 (2021) no. 4, pp. 1265-128. http://geodesic.mathdoc.fr/item/JCA_2021_28_4_JCA_2021_28_4_a15/