A note on generalized four-point inequality
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913629079601152 |
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| author | Petrov, Evgeniy A. Salimov, Ruslan R. |
| author_facet | Petrov, Evgeniy A. Salimov, Ruslan R. |
| contents | In 2017 M. Bessenyei and Z. Páles introduced a definition of a triangle function which generates a concept of a generalized triangle inequality in semimetric spaces. Inspired by this concept we discuss already known inequalities in metric spaces that relate the six distances determined by four points and introduce a definition of a generalized four-point inequality in semimetric spaces. Conditions under which quasisymmetric mappings and quasimöbius mappings between semimetric spaces preserve such inequality are obtained. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_20526 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on generalized four-point inequality Petrov, Evgeniy A. Salimov, Ruslan R. General Topology 54E25, 54C25 In 2017 M. Bessenyei and Z. Páles introduced a definition of a triangle function which generates a concept of a generalized triangle inequality in semimetric spaces. Inspired by this concept we discuss already known inequalities in metric spaces that relate the six distances determined by four points and introduce a definition of a generalized four-point inequality in semimetric spaces. Conditions under which quasisymmetric mappings and quasimöbius mappings between semimetric spaces preserve such inequality are obtained. |
| title | A note on generalized four-point inequality |
| topic | General Topology 54E25, 54C25 |
| url | https://arxiv.org/abs/2412.20526 |