A New Weighted Metric: the Relative Metric I

Details A New Weighted Metric: the Relative Metric I A New Weighted Metric: the Relative Metric I

2001-08-03

arxiv.org/abs/math/0108025v3

Mathematics

Metric Geometry

23 pages

Scientific paper

The M-relative distance, denoted by \rho_M is a generalization of the p-relative distance, which was introduced by Ren-Cang 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.

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