A quantitative version of the converse Taylor theorem: Ck,ω-smoothness
Michal Johanis
Colloquium Mathematicae, Tome 135 (2014), p. 57-64 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:284127 
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     author = {Michal Johanis},
     title = {A quantitative version of the converse Taylor theorem: $C^{k,$\omega$}$-smoothness},
     journal = {Colloquium Mathematicae},
     volume = {135},
     year = {2014},
     pages = {57-64},
     zbl = {1309.46023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm136-1-6}
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Michal Johanis. A quantitative version of the converse Taylor theorem: $C^{k,ω}$-smoothness. Colloquium Mathematicae, Tome 135 (2014) pp. 57-64. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm136-1-6/