Zone diagrams in compact subsets of uniformly convex normed spaces

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Zone diagrams in compact subsets of uniformly convex normed spaces
Original language description
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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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