Reference : A generalization of the concept of distance based on the simplex inequality
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Engineering, computing & technology : Computer science
Computational Sciences
http://hdl.handle.net/10993/34025
A generalization of the concept of distance based on the simplex inequality
English
Kiss, Gergely mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Marichal, Jean-Luc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Teheux, Bruno mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Jun-2018
Beitraege zur Algebra und Geometrie = Contributions to Algebra and Geometry
Springer
59
2
247–266
Yes
International
0138-4821
2191-0383
[en] n-distance ; simplex inequality ; Fermat point ; smallest enclosing sphere
[en] We introduce and discuss the concept of \emph{$n$-distance}, a generalization to $n$ elements of the classical notion of distance obtained by replacing the triangle inequality with the so-called simplex inequality
\[
d(x_1, \ldots, x_n)~\leq~K\, \sum_{i=1}^n d(x_1, \ldots, x_n)_i^z{\,}, \qquad x_1, \ldots, x_n, z \in X,
\]
where $K=1$. Here $d(x_1,\ldots,x_n)_i^z$ is obtained from the function $d(x_1,\ldots,x_n)$ by setting its $i$th variable to $z$. We provide several examples of $n$-distances, and for each of them we investigate the infimum of the set of real numbers $K\in\left]0,1\right]$ for which the inequality above holds. We also introduce a generalization of the concept of $n$-distance obtained by replacing in the simplex inequality the sum function with an arbitrary symmetric function.
University of Luxembourg - UL
R-AGR-0500 > MRO3 > 01/03/2015 - 28/02/2018 > MARICHAL Jean-Luc
Researchers ; Professionals ; Students
http://hdl.handle.net/10993/34025
https://arxiv.org/abs/1611.07826

File(s) associated to this reference

Fulltext file(s):

FileCommentaryVersionSizeAccess
Open access
GeneralizationDistance-Revised.pdfAuthor postprint125.82 kBView/Open
Limited access
PV-GeneralizationDistance.pdfPublisher postprint502.32 kBRequest a copy

Bookmark and Share SFX Query

All documents in ORBilu are protected by a user license.