三角比度量的界和比较不等式  

Bounds and comparison inequalities for the triangular ratio metric

作　　者：贾改莉 张孝惠 JIA Gaili;ZHANG Xiaohui(School of Science,Zhejiang Sci-Tech University,Hangzhou 310018,China)

机构地区：[1]浙江理工大学理学院,杭州310018

出　　处：《浙江理工大学学报（自然科学版）》2020年第6期858-864,共7页Journal of Zhejiang Sci-Tech University(Natural Sciences)

基　　金：This research is supported by National Natural Science Foundation of China(NNSFC)(Grant No.11771400);Science Foundation of Zhejiang Sci-Tech University(ZSTU)(Grant No.16062023-Y)。

摘　　要：研究了三角比度量在单位圆盘内的上下界,分别证明了三角比度量与距离比度量、双曲度量、Cassini度量和Gromov双曲度量等四个度量的比较关系。特别地,证明了三角比度量与这些双曲型度量之间不等式的精确性。The purpose of this paper is to establish upper and lower bounds for the triangular ratio metric,and to present geometric properties of the triangular ratio metric by comparing it with the distance ratio metric,the hyperbolic metric,the Cassinian metric,and a Gromov hyperbolic metric.In particular,we show the sharpness of the inequalities between the triangular ratio metric and these hyperbolic type metrics.

关 键 词：三角比度量 双曲型度量 凸域 

分 类 号：O174.5[理学—数学]