Geodesic
A quantitative version of the converse Taylor theorem: $C^{k,\omega }$-smoothness
Michal Johanis1
1 Department of Mathematical Analysis Charles University Sokolovská 83 186 75 Praha 8, Czech Republic
Colloquium Mathematicum, Tome 136 (2014) no. 1, pp. 57-64.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We prove a uniform version of the converse Taylor theorem in infinite-dimensional spaces with an explicit relation between the moduli of continuity for mappings on a general open domain. We show that if the domain is convex and bounded, then we can extend the estimate up to the boundary.
DOI : 10.4064/cm136-1-6
Keywords: prove uniform version converse taylor theorem infinite dimensional spaces explicit relation between moduli continuity mappings general domain domain convex bounded extend estimate boundary

Michal Johanis 1

1 Department of Mathematical Analysis Charles University Sokolovská 83 186 75 Praha 8, Czech Republic 
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Michal Johanis. A quantitative version of the converse
 Taylor theorem: $C^{k,\omega }$-smoothness. Colloquium Mathematicum, Tome 136 (2014) no. 1, pp. 57-64. doi : 10.4064/cm136-1-6. http://geodesic.mathdoc.fr/articles/10.4064/cm136-1-6/

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