Geodesic
Differentiability of Convex Functions on a Locally Convex Topological Vector Space
Journal of convex analysis, Tome 26 (2019) no. 3, pp. 761-772
Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

We introduce the notion of a smooth set in a locally convex topological vector space and extend Asplund's result on the strong differentiability space. We also establish Gateaux differentiability of a continuous convex function in a locally convex topological vector space. In particular, we extend Mazur's classical theorem on Gateaux differentiability from a separable Banach space to a separable locally convex topological vector space.
Classification : 52A41, 49J50, 46A55
Mots-clés : Topological vector space, smooth set, uniform differentiability, Gateaux differentiability 
@article{JCA_2019_26_3_JCA_2019_26_3_a4,
     author = {X. Y. Zheng and K. F. Ng},
     title = {Differentiability of {Convex} {Functions} on a {Locally} {Convex} {Topological} {Vector} {Space}},
     journal = {Journal of convex analysis},
     pages = {761--772},
     year = {2019},
     volume = {26},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2019_26_3_JCA_2019_26_3_a4/}
}
TY  - JOUR
AU  - X. Y. Zheng
AU  - K. F. Ng
TI  - Differentiability of Convex Functions on a Locally Convex Topological Vector Space
JO  - Journal of convex analysis
PY  - 2019
SP  - 761
EP  - 772
VL  - 26
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JCA_2019_26_3_JCA_2019_26_3_a4/
ID  - JCA_2019_26_3_JCA_2019_26_3_a4
ER  - 
%0 Journal Article
%A X. Y. Zheng
%A K. F. Ng
%T Differentiability of Convex Functions on a Locally Convex Topological Vector Space
%J Journal of convex analysis
%D 2019
%P 761-772
%V 26
%N 3
%U http://geodesic.mathdoc.fr/item/JCA_2019_26_3_JCA_2019_26_3_a4/
%F JCA_2019_26_3_JCA_2019_26_3_a4
X. Y. Zheng; K. F. Ng. Differentiability of Convex Functions on a Locally Convex Topological Vector Space. Journal of convex analysis, Tome 26 (2019) no. 3, pp. 761-772. http://geodesic.mathdoc.fr/item/JCA_2019_26_3_JCA_2019_26_3_a4/