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Ukrainian Mathematical Journal

, Volume 70, Issue 9, pp 1456–1466 | Cite as

On the Equicontinuity of One Family of Inverse Mappings in Terms of Prime Ends

  • R. R. Salimov
  • E. A. Sevost’yanov
Article
  • 18 Downloads

For a class of mappings satisfying upper modular estimates with respect to the families of curves, we study the local behavior of the corresponding inverse mappings. In terms of prime ends, we prove that the families of these homeomorphisms are equicontinuous (normal) in the closure of a given domain.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • R. R. Salimov
    • 1
  • E. A. Sevost’yanov
    • 2
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine
  2. 2.I. Franko Zhitomir State UniversityZhitomirUkraine

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