The Quasisymmetric Mappings under the Quasihyperbolic Metric in Real Banach Spaces
Suppose that E,E′ are Q-regular Banach spaces, that G⊂E and G′⊂E′ are domains, and that f:G⟶G′ is a homeomorphism. The aim of this study is to prove that the quasisymmetric mapping under the quasihyperbolic metric is equivalent to the freely quasiconformal mapping under the condition E,E′ being Q-re...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/5938029 |
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| _version_ | 1849415031974789120 |
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| author | Caicai Hu Liang Guo |
| author_facet | Caicai Hu Liang Guo |
| author_sort | Caicai Hu |
| collection | DOAJ |
| description | Suppose that E,E′ are Q-regular Banach spaces, that G⊂E and G′⊂E′ are domains, and that f:G⟶G′ is a homeomorphism. The aim of this study is to prove that the quasisymmetric mapping under the quasihyperbolic metric is equivalent to the freely quasiconformal mapping under the condition E,E′ being Q-regular Banach spaces. This result is a partial solution to an open problem raised by Väisälä. |
| format | Article |
| id | doaj-art-6a00a14ec75c45f0a7eb529db35cca99 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-6a00a14ec75c45f0a7eb529db35cca992025-08-20T03:33:39ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/5938029The Quasisymmetric Mappings under the Quasihyperbolic Metric in Real Banach SpacesCaicai Hu0Liang Guo1MOE-LCSMMOE-LCSMSuppose that E,E′ are Q-regular Banach spaces, that G⊂E and G′⊂E′ are domains, and that f:G⟶G′ is a homeomorphism. The aim of this study is to prove that the quasisymmetric mapping under the quasihyperbolic metric is equivalent to the freely quasiconformal mapping under the condition E,E′ being Q-regular Banach spaces. This result is a partial solution to an open problem raised by Väisälä.http://dx.doi.org/10.1155/2022/5938029 |
| spellingShingle | Caicai Hu Liang Guo The Quasisymmetric Mappings under the Quasihyperbolic Metric in Real Banach Spaces Journal of Mathematics |
| title | The Quasisymmetric Mappings under the Quasihyperbolic Metric in Real Banach Spaces |
| title_full | The Quasisymmetric Mappings under the Quasihyperbolic Metric in Real Banach Spaces |
| title_fullStr | The Quasisymmetric Mappings under the Quasihyperbolic Metric in Real Banach Spaces |
| title_full_unstemmed | The Quasisymmetric Mappings under the Quasihyperbolic Metric in Real Banach Spaces |
| title_short | The Quasisymmetric Mappings under the Quasihyperbolic Metric in Real Banach Spaces |
| title_sort | quasisymmetric mappings under the quasihyperbolic metric in real banach spaces |
| url | http://dx.doi.org/10.1155/2022/5938029 |
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