Geodesic
Spherically Convex Sets and Spherically Convex Functions
Journal of convex analysis, Tome 28 (2021) no. 1, pp. 103-122
Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

We define first the spherical convexity of sets and functions on general curved surfaces by an analytic approach. Then we study several kinds of properties of spherically convex sets and functions. Several analogies of the results for convex sets and convex functions on Euclidean spaces are established or rediscovered for spherically convex sets and spherically convex functions, such as the Radon-type, Helly-type, Carathéodory-type and Minkowski-type theorems for spherically convex sets, and the Jensen's inequality for spherically convex functions etc. The results obtained here might have applications in some areas, e.g. in the optimization theory on general spherical spaces.
Classification : 52A55, 52A20, 52A35, 52A41
Mots-clés : Spherical convexity, Helly theorem, Carathéodory theorem, Jensen's inequality 
@article{JCA_2021_28_1_JCA_2021_28_1_a8,
     author = {Q. Guo and Y. Peng},
     title = {Spherically {Convex} {Sets} and {Spherically} {Convex} {Functions}},
     journal = {Journal of convex analysis},
     pages = {103--122},
     year = {2021},
     volume = {28},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2021_28_1_JCA_2021_28_1_a8/}
}
TY  - JOUR
AU  - Q. Guo
AU  - Y. Peng
TI  - Spherically Convex Sets and Spherically Convex Functions
JO  - Journal of convex analysis
PY  - 2021
SP  - 103
EP  - 122
VL  - 28
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JCA_2021_28_1_JCA_2021_28_1_a8/
ID  - JCA_2021_28_1_JCA_2021_28_1_a8
ER  - 
%0 Journal Article
%A Q. Guo
%A Y. Peng
%T Spherically Convex Sets and Spherically Convex Functions
%J Journal of convex analysis
%D 2021
%P 103-122
%V 28
%N 1
%U http://geodesic.mathdoc.fr/item/JCA_2021_28_1_JCA_2021_28_1_a8/
%F JCA_2021_28_1_JCA_2021_28_1_a8
Q. Guo; Y. Peng. Spherically Convex Sets and Spherically Convex Functions. Journal of convex analysis, Tome 28 (2021) no. 1, pp. 103-122. http://geodesic.mathdoc.fr/item/JCA_2021_28_1_JCA_2021_28_1_a8/