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Relative Quasisymmetry and Quasimöbius Mappings in Quasi-metric Spaces

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Abstract

The aim of this paper is to investigate the relationship between relative quasisymmetry and quasimöbius in quasi-metric spaces, and show that a homeomorphism f is η-quasisymmetric relative to A if and only if it is θ-quasimöbius relative to A between two both bounded quasi-metric spaces, where A ⊆ X and X is a quasi-metric space.

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Acknowledgements

The authors thank the referee for their careful reading and valuable comments that led to the improvement of the paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550001, P. R. China

    Hong Jun Liu & Yue Fan

  2. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, P. R. China

    Xiao Jun Huang

Authors
  1. Hong Jun Liu
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  2. Xiao Jun Huang
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  3. Yue Fan
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Corresponding author

Correspondence to Hong Jun Liu.

Additional information

Supported by National Natural Science Foundation of China (Grant Nos. 11671057, 11901136), the Guizhou Provincial Science and Technology Foundation (Grant No. [2020] 1Y003) and the PhD research startup foundation of Guizhou Normal University (Grant No. 11904/0517078)

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Liu, H.J., Huang, X.J. & Fan, Y. Relative Quasisymmetry and Quasimöbius Mappings in Quasi-metric Spaces. Acta. Math. Sin.-English Ser. 38, 547–559 (2022). https://doi.org/10.1007/s10114-022-1003-z

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  • DOI: https://doi.org/10.1007/s10114-022-1003-z

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