Abstract: The class of multivalued mappings with bounded angular distortion (BAD) property in metric spaces can be considered as a multivalued analog for quasimöbius mappings. We study the connections between quasimeromorphic self-mappings of X = R ̄^n and multivalued mappings F : X → 2X with BAD property. The main result of the paper concerns the multivalued mappings F : D → 2^C with BAD property of a domain D ⊂ C ̄. If the image F(x) of each point x ∈ D is either a point or a continuum with bounded turning then F is proved to be a single-valued quasimobius mapping. The crucial point in the proof of this result is the local connectedness of the set F(X) for the multivalued continuous mapping F : X → 2^Y with BAD property. We obtain sufficient conditions providing F(X) to have local connectedness or bounded turning property in the most general case.

Cite: Abrosimov N.V. , Aseev V.V.
Multivalued quasimöbius property and bounded turning
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2023. V.20. N2. P.1185-1199. DOI: 10.33048/semi.2023.20.073 WOS Scopus РИНЦ

Dates:

Submitted:	Oct 1, 2023
Published print:	Nov 20, 2023
Published online:	Nov 20, 2023

Identifiers:

Web of science:	WOS:001102183700002
Scopus:	2-s2.0-85179984008
Elibrary:	82134659

Citing: Пока нет цитирований

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