一个新的加权度量：相对度量I
A New Weighted Metric: the Relative Metric I
摘要：
M-相对距离（记为ρ_M）是李仁仓提出的p-相对距离的推广。给出了ρ_M是度量的充要条件。在两种特殊情况下，我们得到完整的度量的特征。我们还提出了一种方法，将结果扩展到度量敏感的域中，它们被定义，从而找到一些连接到以前研究的度量。独立兴趣的一个辅助结果是与第4节中的Pittenger不等式有关的一个不等式。
英文摘要：
The 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
