Functions on a Convex Set which are Both ω-Semiconvex and ω-Semiconcave II

Kód výsledku v 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>

Výsledek na webu

<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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Jazyk výsledku

angličtina

Název v původním jazyce

Functions on a Convex Set which are Both ω-Semiconvex and ω-Semiconcave II

Popis výsledku v původním jazyce

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&lt;sup&gt;n&lt;/sup&gt; 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&lt;inf&gt;tRIGHTWARDS ARROWoo&lt;/inf&gt; ω(t) = oo, f is both semiconvex and semiconcave with modulus ω and f NOT AN ELEMENT OF C&lt;sup&gt;1,ω&lt;/sup&gt;(G). Here we improve the previous result as follows: If G is as above and ω(t) = t&lt;sup&gt;α&lt;/sup&gt; 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&lt;sup&gt;1,α&lt;/sup&gt;(G). This result has immediate consequences concerning a first-order quantitative converse Taylor theorem and the problem whether f SMALL ELEMENT OF C&lt;sup&gt;1,α&lt;/sup&gt;(G) whenever f is smooth in a corresponding sense on all lines.

Název v anglickém jazyce

Functions on a Convex Set which are Both ω-Semiconvex and ω-Semiconcave II

Popis výsledku anglicky

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&lt;sup&gt;n&lt;/sup&gt; 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&lt;inf&gt;tRIGHTWARDS ARROWoo&lt;/inf&gt; ω(t) = oo, f is both semiconvex and semiconcave with modulus ω and f NOT AN ELEMENT OF C&lt;sup&gt;1,ω&lt;/sup&gt;(G). Here we improve the previous result as follows: If G is as above and ω(t) = t&lt;sup&gt;α&lt;/sup&gt; 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&lt;sup&gt;1,α&lt;/sup&gt;(G). This result has immediate consequences concerning a first-order quantitative converse Taylor theorem and the problem whether f SMALL ELEMENT OF C&lt;sup&gt;1,α&lt;/sup&gt;(G) whenever f is smooth in a corresponding sense on all lines.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

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

2363-6394

Svazek periodika

35

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

20

Strana od-do

447-466

Kód UT WoS článku

001413936200006

EID výsledku v databázi Scopus

2-s2.0-105006551094