Functional Inequalities for Metric-Preserving Functions with Respect to Intrinsic Metrics of Hyperbolic Type
Functional Inequalities for Metric-Preserving Functions with Respect to Intrinsic Metrics of Hyperbolic Type
复制标题
关于双曲型内建度量的保度量函数的函数不等式
DOI：
10.3390/sym13112072
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
M. Mocanu
中科院分区：
文献类型：
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作者：
M. Mocanu
我们得到了函数的功能不等式，这是度量保持关于以下之一的内在度量在一个典型的平面域：双曲度量或三角比度量的一些限制，分别为Barrlund度量。次可加性被证明是一个基本性质，它被每一个关于双曲度量保持度量的函数所拥有，也被每一个关于三角比度量或Barrlund度量的某种限制保持度量的函数与某个特定函数的复合所拥有。我们部分回答了一个公开的问题，证明双曲反正切是度量保持相对于限制的三角形比率度量的单位磁盘上的径向段和圆中心在原点。
We obtain functional inequalities for functions which are metric-preserving with respect to one of the following intrinsic metrics in a canonical plane domain: hyperbolic metric or some restrictions of the triangular ratio metric, respectively, of a Barrlund metric. The subadditivity turns out to be an essential property, being possessed by every function that is metric-preserving with respect to the hyperbolic metric and also by the composition with some specific function of every function that is metric-preserving with respect to some restriction of the triangular ratio metric or of a Barrlund metric. We partially answer an open question, proving that the hyperbolic arctangent is metric-preserving with respect to the restrictions of the triangular ratio metric on the unit disk to radial segments and to circles centered at origin.
一种新的内在度量和拟正则映射
DOI：
10.1007/s40627-021-00066-z
发表时间：
2021
期刊：
Complex Analysis and its Synergies
影响因子：
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作者：
Fujimura Masayo;Mocanu Marcelina;Vuorinen Matti
通讯作者：
Vuorinen Matti