On equicontinuity of families of mappings with one normalization condition by the prime ends

  • N. S. Ilkevych Zhytomyr Ivan Franko State University
  • E. A. Sevost’yanov Zhytomyr Ivan Franko State University
Keywords: mappings with finite and bounded distortion, prime ends, local and boundary behavior of mappings

Abstract

UDC 517.5

We study mappings with branching that satisfy certain conditions of distortion for the modulus of paths families. Under the conditions that the domain of definition of mappings has a weakly flat boundary, the mapped domain is regular, and the majorant responsible for the distortion of modulus of the families of paths is integrable; it is proved that the families of all specified mappings with one normalization condition are equicontinuous in the closure of the given domain.

Author Biography

N. S. Ilkevych, Zhytomyr Ivan Franko State University

 

 

 

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Published
07.07.2022
How to Cite
Ilkevych, N. S., and E. A. Sevost’yanov. “On Equicontinuity of Families of Mappings With One Normalization Condition by the Prime Ends”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, no. 6, July 2022, pp. 817 -25, doi:10.37863/umzh.v74i6.6887.
Section
Research articles