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arXiv · 2412.20526

A note on generalized four-point inequality

Evgeniy A. Petrov·Ruslan R. Salimov
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Abstract

In 2017 M. Bessenyei and Z. P\'ales 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 quasim\"{o}bius mappings between semimetric spaces preserve such inequality are obtained.

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Evgeniy A. Petrov, Ruslan R. Salimov. 2024-12-29. A note on generalized four-point inequality. https://doi.org/10.1007/s10958-023-06507-w

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