Functional Inequalities for Metric-Preserving Functions with Respect to Intrinsic Metrics of Hyperbolic Type

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...

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Autor principal:	Marcelina Mocanu
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	metric-preserving function subadditive function intrinsic metric Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/4c1303d724df4bee87df3f6969860b31
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spelling	oai:doaj.org-article:4c1303d724df4bee87df3f6969860b312021-11-25T19:06:31ZFunctional Inequalities for Metric-Preserving Functions with Respect to Intrinsic Metrics of Hyperbolic Type10.3390/sym131120722073-8994https://doaj.org/article/4c1303d724df4bee87df3f6969860b312021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2072https://doaj.org/toc/2073-8994We 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.Marcelina MocanuMDPI AGarticlemetric-preserving functionsubadditive functionintrinsic metricMathematicsQA1-939ENSymmetry, Vol 13, Iss 2072, p 2072 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	metric-preserving function subadditive function intrinsic metric Mathematics QA1-939
spellingShingle	metric-preserving function subadditive function intrinsic metric Mathematics QA1-939 Marcelina Mocanu Functional Inequalities for Metric-Preserving Functions with Respect to Intrinsic Metrics of Hyperbolic Type
description	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.
format	article
author	Marcelina Mocanu
author_facet	Marcelina Mocanu
author_sort	Marcelina Mocanu
title	Functional Inequalities for Metric-Preserving Functions with Respect to Intrinsic Metrics of Hyperbolic Type
title_short	Functional Inequalities for Metric-Preserving Functions with Respect to Intrinsic Metrics of Hyperbolic Type
title_full	Functional Inequalities for Metric-Preserving Functions with Respect to Intrinsic Metrics of Hyperbolic Type
title_fullStr	Functional Inequalities for Metric-Preserving Functions with Respect to Intrinsic Metrics of Hyperbolic Type
title_full_unstemmed	Functional Inequalities for Metric-Preserving Functions with Respect to Intrinsic Metrics of Hyperbolic Type
title_sort	functional inequalities for metric-preserving functions with respect to intrinsic metrics of hyperbolic type
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/4c1303d724df4bee87df3f6969860b31
work_keys_str_mv	AT marcelinamocanu functionalinequalitiesformetricpreservingfunctionswithrespecttointrinsicmetricsofhyperbolictype
_version_	1718410275700342784

Functional Inequalities for Metric-Preserving Functions with Respect to Intrinsic Metrics of Hyperbolic Type

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