A Remark on the Nullness of Boundaries of Uniformly Prox-Regular Sets in Banach Spaces

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10510979" target="_blank" >RIV/00216208:11320/25:10510979 - isvavai.cz</a>

Result on the web

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=OPCzrZWCrT" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=OPCzrZWCrT</a>

DOI - Digital Object Identifier

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Result language

angličtina

Original language name

A Remark on the Nullness of Boundaries of Uniformly Prox-Regular Sets in Banach Spaces

Original language description

We prove that, in any separable uniformly smooth Banach space, the boundary of every a-convex set (in the Efimov-Stechkin sense) is Gamma-null (in the Lindenstrauss-Preiss sense). Using well-known results, we obtain that the same is true for proximally smooth sets (in the sense of Clarke, Stern and Wolenski) and for uniformly prox-regular sets (in the sense of Poliquin, Rockafellar and Thibault) in any separable Banach space which is both uniformly convex and uniformly smooth.

Czech name

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Czech description

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Type

J_imp - 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

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2025

Confidentiality

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

Name of the periodical

Journal of Convex Analysis

ISSN

0944-6532

e-ISSN

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Volume of the periodical

32

Issue of the periodical within the volume

3

Country of publishing house

DE - GERMANY

Number of pages

6

Pages from-to

921-926

UT code for WoS article

001414490700017

EID of the result in the Scopus database

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