2001/08/03 by Peter Hästö, Peter A. Hasto, Hasto, Peter A.
Computer Science · Mathematics · #26D07 #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Matrix Theory and Algorithms #Metric Geometry (math.MG) #Point processes and geometric inequalities #Primary 39B62 #Secondary 51F99 #math.CA #math.MG #msc:26D07 #msc:39B62 #msc:51F99
paper · pdf · doi:10.48550/arxiv.math/0108025
23 pages
openalex publication_date 2001/08/03 · arxiv created 2002/02/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The M-relative distance, denoted by ρM is a generalization of the p-relative distance, which was introduced by Ren-Cang Li. We establish necessary and sufficient conditions under which ρM is a metric. In two special cases we derive complete characterizations of the metric. We also present a way of extending the results to metrics sensitive to the domain in which they are defined, thus finding some connections to previously studied metrics. An auxiliary result of independent interest is an inequality related to Pittenger's inequality in Section 4.