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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

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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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

  • 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