# A New Weighted Metric: the Relative Metric I

@inproceedings{Hasto2001ANW, title={A New Weighted Metric: the Relative Metric I}, author={Peter A. Hasto}, year={2001} }

The M –relative distance , denoted by ρ M is a generalization of the p –relative distance, which was introduced in [10]. 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…

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