A New Weighted Metric: the Relative Metric I
Abstract
The Mrelative distance, denoted by \rho_M is a generalization of the prelative distance, which was introduced by RenCang Li. We establish necessary and sufficient conditions under which \rho_M 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 August 2001
 arXiv:
 arXiv:math/0108025
 Bibcode:
 2001math......8025H
 Keywords:

 Metric Geometry;
 Classical Analysis and ODEs;
 Primary 39B62;
 Secondary 51F99;
 26D07
 EPrint:
 23 pages