A note on generalized four-point inequality
General Topology
2024-12-31 v1
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.
Cite
@article{arxiv.2412.20526,
title = {A note on generalized four-point inequality},
author = {Evgeniy A. Petrov and Ruslan R. Salimov},
journal= {arXiv preprint arXiv:2412.20526},
year = {2024}
}
Comments
19 pages