Zone diagrams in compact subsets of uniformly convex normed spaces

0380717 - MÚ 2013 RIV IL eng J - Článek v odborném periodiku
Kopecká, Eva - Reem, D. - Reich, S.
Zone diagrams in compact subsets of uniformly convex normed spaces.
Israel Journal of Mathematics. Roč. 188, č. 1 (2012), s. 1-23. ISSN 0021-2172. E-ISSN 1565-8511
Institucionální podpora: RVO:67985840
Klíčová slova: zone diagrams
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.646, rok: 2012
http://www.springerlink.com/content/w671758286258j62/

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.
Trvalý link: http://hdl.handle.net/11104/0211354