Geodesic
Criteria for Convexity of Closed Sets in Banach Spaces
Informatics and Automation, Optimal control and differential equations, Tome 304 (2019), pp. 205-220

Voir la notice de l'article provenant de la source Math-Net.Ru

Criteria for the convexity of closed sets in general Banach spaces in terms of the Clarke and Bouligand tangent cones are proved. In the case of uniformly convex spaces, these convexity criteria are stated in terms of proximal normal cones. These criteria are used to derive sufficient conditions for the convexity of the images of convex sets under nonlinear mappings and multifunctions. 
@article{TRSPY_2019_304_a12,
     author = {Yu. S. Ledyaev},
     title = {Criteria for {Convexity} of {Closed} {Sets} in {Banach} {Spaces}},
     journal = {Informatics and Automation},
     pages = {205--220},
     publisher = {mathdoc},
     volume = {304},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2019_304_a12/}
}
TY  - JOUR
AU  - Yu. S. Ledyaev
TI  - Criteria for Convexity of Closed Sets in Banach Spaces
JO  - Informatics and Automation
PY  - 2019
SP  - 205
EP  - 220
VL  - 304
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2019_304_a12/
LA  - ru
ID  - TRSPY_2019_304_a12
ER  - 
%0 Journal Article
%A Yu. S. Ledyaev
%T Criteria for Convexity of Closed Sets in Banach Spaces
%J Informatics and Automation
%D 2019
%P 205-220
%V 304
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2019_304_a12/
%G ru
%F TRSPY_2019_304_a12
Yu. S. Ledyaev. Criteria for Convexity of Closed Sets in Banach Spaces. Informatics and Automation, Optimal control and differential equations, Tome 304 (2019), pp. 205-220. http://geodesic.mathdoc.fr/item/TRSPY_2019_304_a12/