Zone diagrams in compact subsets of uniformly convex normed spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F12%3A00380717" target="_blank" >RIV/67985840:_____/12:00380717 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s11856-011-0094-5" target="_blank" >http://dx.doi.org/10.1007/s11856-011-0094-5</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11856-011-0094-5" target="_blank" >10.1007/s11856-011-0094-5</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Zone diagrams in compact subsets of uniformly convex normed spaces

Popis výsledku v původním jazyce

A zone diagram is a relatively new concept which has emerged in computational geometry and is related to Voronoi diagrams. Formally, it is a fixed point of a certain mapping, and neither its uniqueness nor its existence are obvious in advance. It has been studied by several authors, starting with T. Asano, J. Matousek and T. Tokuyama, who considered the Euclidean plane with singleton sites, and proved the existence and uniqueness of zone diagrams there. In the present paper we prove the existence of zone diagrams with respect to finitely many pairwise disjoint compact sites contained in a compact and convex subset of a uniformly convex normed space, provided that either the sites or the convex subset satisfy a certain mild condition.

Název v anglickém jazyce

Zone diagrams in compact subsets of uniformly convex normed spaces

Popis výsledku anglicky

A zone diagram is a relatively new concept which has emerged in computational geometry and is related to Voronoi diagrams. Formally, it is a fixed point of a certain mapping, and neither its uniqueness nor its existence are obvious in advance. It has been studied by several authors, starting with T. Asano, J. Matousek and T. Tokuyama, who considered the Euclidean plane with singleton sites, and proved the existence and uniqueness of zone diagrams there. In the present paper we prove the existence of zone diagrams with respect to finitely many pairwise disjoint compact sites contained in a compact and convex subset of a uniformly convex normed space, provided that either the sites or the convex subset satisfy a certain mild condition.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

Israel Journal of Mathematics

ISSN

0021-2172

e-ISSN

—

Svazek periodika

188

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

IL - Stát Izrael

Počet stran výsledku

23

Strana od-do

1-23

Kód UT WoS článku

000305386100001

EID výsledku v databázi Scopus

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