Quasisymmetric mappings in b-metric spaces
Evgeniy A. Petrov, Ruslan R. Salimov
TL;DR
This paper investigates quasisymmetric mappings in b-metric spaces, providing new diameter ratio estimates, generalizing existing inequalities, and exploring conditions for the image space to retain b-metric properties.
Contribution
It introduces a novel diameter ratio estimation for quasisymmetric images and establishes conditions for the preservation of b-metric structure under such mappings.
Findings
New estimation for diameter ratios in b-metric spaces
Generalization of Tukia-V"{a}is"{a}l"{a} inequality
Conditions for images of b-metric spaces to remain b-metric
Abstract
Considering quasisymmetric mappings between b-metric spaces we have found a new estimation for the ratio of diameters of two subsets which are images of two bounded subsets. This result generalizes the well-known Tukia-V\"{a}is\"{a}l\"{a} inequality. The condition under which the image of a b-metric space under quasisymmetry is also a b-metric space is established. Moreover, the latter question is investigated for additive metric spaces.
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