Arc length associated with generalized distance functions
type: Item
instance of: scholarly article
title: Arc length associated with generalized distance functions
zbMATH Open document ID: 1201.53017
author: Hérica Sánchez-Larios
author: Servio Guillén-Burguete
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-07-20T00:00:00Z
review text: The authors consider generalized distance functions \(d\) which do not satisfy the usual properties except that \(d(x, x)= 0\) for any \(x\). An arc length of rectifiable curves is introduced in the usual manner. Under an additional assumption on the one-sided directional derivative an explicit expression of the arc length is obtained in terms of an integral. Finally an example is given for a non-positive definite and asymmetric distance function.
Mathematics Subject Classification ID: 53B20
Mathematics Subject Classification ID: 53C70
Mathematics Subject Classification ID: 53C60
Mathematics Subject Classification ID: 53B40
zbMATH DE Number: 5757937
zbMATH Keywords: energy
zbMATH Keywords: distance function
zbMATH Keywords: triangle inequality
reviewed by: Wolfgang Kühnel
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.04.030
OpenAlex ID: W1995923781
cites work: Q3128806
cites work: The geometry of Finsler spaces
cites work: Q5705858
cites work: The P-Centroid Problem on an Inclined Plane
cites work: Arc length in metric and Finsler manifolds
cites work: Q4078263
cites work: Relation between metric spaces and Finsler spaces
DOI: 10.1016/J.JMAA.2010.04.030
description: scientific article; zbMATH DE number 5757937