Functions on a Convex Set which are Both ω-Semiconvex and ω-Semiconcave II
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10511055" target="_blank" >RIV/00216208:11320/25:10511055 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=8-5L8eeu00" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=8-5L8eeu00</a>
DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Functions on a Convex Set which are Both ω-Semiconvex and ω-Semiconcave II
Original language description
In a recent article [Functions on a convex set which are both ω-semiconvex and ω-semiconcave I, J. Convex Analysis 29 (2022) 837-856] we proved with L. Zajíček that if G SUBSET OF R<sup>n</sup> is an unbounded open convex set that does not contain a translation of a convex cone with non-empty interior, then there exist f : G RIGHTWARDS ARROW R and a concave modulus ω such that lim<inf>tRIGHTWARDS ARROWoo</inf> ω(t) = oo, f is both semiconvex and semiconcave with modulus ω and f NOT AN ELEMENT OF C<sup>1,ω</sup>(G). Here we improve the previous result as follows: If G is as above and ω(t) = t<sup>α</sup> for some α SMALL ELEMENT OF (0, 1), then there exists f : G RIGHTWARDS ARROW R that is both semiconvex and semiconcave with modulus ω and f NOT AN ELEMENT OF C<sup>1,α</sup>(G). This result has immediate consequences concerning a first-order quantitative converse Taylor theorem and the problem whether f SMALL ELEMENT OF C<sup>1,α</sup>(G) whenever f is smooth in a corresponding sense on all lines.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Convex Analysis
ISSN
0944-6532
e-ISSN
2363-6394
Volume of the periodical
35
Issue of the periodical within the volume
2
Country of publishing house
DE - GERMANY
Number of pages
20
Pages from-to
447-466
UT code for WoS article
001413936200006
EID of the result in the Scopus database
2-s2.0-105006551094