A note on generalized four-point inequality
arXiv:2412.20526 · doi:10.1007/s10958-023-06507-w
Abstract
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.
19 pages