Geodesic
On vector functions of bounded convexity
Mathematica Bohemica, Tome 133 (2008) no. 3, pp. 321-335.

Voir la notice de l'article dans Czech Digital Mathematics Library

Let X be a normed linear space. We investigate properties of vector functions F:[a,b]→X of bounded convexity. In particular, we prove that such functions coincide with the delta-convex mappings admitting a Lipschitz control function, and that convexity KabF is equal to the variation of F+′ on [a,b). As an application, we give a simple alternative proof of an unpublished result of the first author, containing an estimate of convexity of a composed mapping.
DOI : 10.21136/MB.2008.140621
Classification : 26A99, 47H99
Mots-clés : bounded convexity; delta-convex mapping; bounded variation; Banach space 
@article{10_21136_MB_2008_140621,
     author = {Vesel\'y, Libor and Zaj{\'\i}\v{c}ek, Lud\v{e}k},
     title = {On vector functions of bounded convexity},
     journal = {Mathematica Bohemica},
     pages = {321--335},
     publisher = {mathdoc},
     volume = {133},
     number = {3},
     year = {2008},
     doi = {10.21136/MB.2008.140621},
     mrnumber = {2494785},
     zbl = {1199.47242},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2008.140621/}
}
TY  - JOUR
AU  - Veselý, Libor
AU  - Zajíček, Luděk
TI  - On vector functions of bounded convexity
JO  - Mathematica Bohemica
PY  - 2008
SP  - 321
EP  - 335
VL  - 133
IS  - 3
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2008.140621/
DO  - 10.21136/MB.2008.140621
LA  - en
ID  - 10_21136_MB_2008_140621
ER  - 
%0 Journal Article
%A Veselý, Libor
%A Zajíček, Luděk
%T On vector functions of bounded convexity
%J Mathematica Bohemica
%D 2008
%P 321-335
%V 133
%N 3
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2008.140621/
%R 10.21136/MB.2008.140621
%G en
%F 10_21136_MB_2008_140621
Veselý, Libor; Zajíček, Luděk. On vector functions of bounded convexity. Mathematica Bohemica, Tome 133 (2008) no. 3, pp. 321-335. doi : 10.21136/MB.2008.140621. https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2008.140621/

Cité par Sources :