Functions on a Convex Set which are both omega-Semiconvex and omega-Semiconcave

Kód výsledku v 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>

Výsledek na webu

<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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Jazyk výsledku

angličtina

Název v původním jazyce

Functions on a Convex Set which are both omega-Semiconvex and omega-Semiconcave

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Functions on a Convex Set which are both omega-Semiconvex and omega-Semiconcave

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-11058S" target="_blank" >GA18-11058S: Zobecněná konvexita v geometrii a analýze</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Convex Analysis

ISSN

0944-6532

e-ISSN

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Svazek periodika

29

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

20

Strana od-do

837-856

Kód UT WoS článku

000840554100013

EID výsledku v databázi Scopus

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