Sharp univalence and sharp univalent covering domains for the class of holomorphic self-maps of a disc with two fixed boundary points

The class of holomorphic self-maps of the unit disc with two fixed boundary points, one of which is attracting, is under consideration. Maximal univalence and univalent covering domains are found for the functions in this class that satisfy a bound on the value of the angular derivative at the repel...

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Bibliographic Details
Published inSbornik. Mathematics Vol. 216; no. 4; pp. 494 - 514
Main Authors Kudryavtseva, Olga Sergeevna, Solodov, Aleksei Petrovich
Format Journal Article
LanguageEnglish
Published 2025
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Summary:The class of holomorphic self-maps of the unit disc with two fixed boundary points, one of which is attracting, is under consideration. Maximal univalence and univalent covering domains are found for the functions in this class that satisfy a bound on the value of the angular derivative at the repelling boundary point. Bibliography: 17 titles.
ISSN:1064-5616
1468-4802
DOI:10.4213/sm10118e