Geodesic
Uniformly Convex Metric Spaces
Analysis and Geometry in Metric Spaces, Tome 2 (2014) no. 1.

Voir la notice de l'article provenant de la source The Polish Digital Mathematics Library

In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit a generalized convexity of the metric from a fixed point. Using a (nearly) uniform convexity property a simple proof of reflexivity is presented and a weak topology of such spaces is analyzed. This topology, called coconvex topology, agrees with the usually weak topology in Banach spaces. An example of a CAT(0)-space with weak topology which is not Hausdorff is given. In the end existence and uniqueness of generalized barycenters is shown, an application to isometric group actions is given and a Banach-Saks property is proved.
Mots-clés : convex metric spaces, weak topologies, generalized barycenters, Banach-Saks property 
@article{AGMS_2014_2_1_a1,
     author = {Kell, Martin},
     title = {Uniformly {Convex} {Metric} {Spaces}},
     journal = {Analysis and Geometry in Metric Spaces},
     publisher = {mathdoc},
     volume = {2},
     number = {1},
     year = {2014},
     zbl = {1311.53062},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AGMS_2014_2_1_a1/}
}
TY  - JOUR
AU  - Kell, Martin
TI  - Uniformly Convex Metric Spaces
JO  - Analysis and Geometry in Metric Spaces
PY  - 2014
VL  - 2
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AGMS_2014_2_1_a1/
LA  - en
ID  - AGMS_2014_2_1_a1
ER  - 
%0 Journal Article
%A Kell, Martin
%T Uniformly Convex Metric Spaces
%J Analysis and Geometry in Metric Spaces
%D 2014
%V 2
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AGMS_2014_2_1_a1/
%G en
%F AGMS_2014_2_1_a1
Kell, Martin. Uniformly Convex Metric Spaces. Analysis and Geometry in Metric Spaces, Tome 2 (2014) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2014_2_1_a1/