• Corpus ID: 119134743

A New Weighted Metric: the Relative Metric I

  title={A New Weighted Metric: the Relative Metric I},
  author={Peter A. Hasto},
  • P. Hasto
  • Published 3 August 2001
  • Mathematics
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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