A New Weighted Metric: the Relative Metric I

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dc.creatorHasto, Peter A.
dc.date2001-08-03
dc.date2002-02-26
dc.date.accessioned2026-07-07T04:42:51Z
dc.date.available2026-07-07T04:42:51Z
dc.descriptionThe M-relative distance, denoted by ρ_M is a generalization of the p-relative distance, which was introduced by Ren-Cang Li. We establish necessary and sufficient conditions under which ρ_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.
dc.description23 pages
dc.identifierhttps://arxiv.org/abs/math/0108025
dc.identifierhttp://arxiv.org/abs/math/0108025
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61965
dc.subjectMetric Geometry
dc.subjectClassical Analysis and ODEs
dc.subjectPrimary 39B62, Secondary 51F99, 26D07
dc.titleA New Weighted Metric: the Relative Metric I
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