Functions on a Convex Set which are both omega-Semiconvex and omega-Semiconcave
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10456380" target="_blank" >RIV/00216208:11320/22:10456380 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=iwYac4a-Om" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=iwYac4a-Om</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 omega-Semiconvex and omega-Semiconcave
Original language description
Let G subset of R-n be an open convex set which is either bounded or contains a translation of a convex cone with nonempty interior. It is known that, for every modulus omega, every function on G which is both semiconvex and semiconcave with modulus omega is (globally) C-1,C-omega-smooth. We show that this result is optimal in the sense that the assumption on G cannot be relaxed. We also present direct short proofs of the above mentioned result and of some its quantitative versions. Our results have immediate consequences concerning (i) a first-order quantitative converse Taylor theorem and (ii) the problem whether f is an element of C-1,C-omega(G) whenever f is continuous and smooth in a corresponding sense on all lines. We hope that these consequences are of an independent interest.
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
<a href="/en/project/GA18-11058S" target="_blank" >GA18-11058S: Generalized convexity in geometry and analysis</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
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
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Volume of the periodical
29
Issue of the periodical within the volume
3
Country of publishing house
DE - GERMANY
Number of pages
20
Pages from-to
837-856
UT code for WoS article
000840554100013
EID of the result in the Scopus database
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