Abstract
In 2017, M. Bessenyei and Z. Páles [1] introduced a definition of a triangle function that 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 six distances determined by four points and introduce a definition of the generalized four-point inequality in semimetric spaces. Conditions under which quasisymmetric mappings and quasi-Möbius mappings between semimetric spaces preserve such an inequality are obtained.
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