 |
|
|
|
|
|
Asymptotically sharp two-sided estimate for domains of univalence of holomorphic self-maps of a disc with an invariant diameter O. S. Kudryavtsevaab, A. P. Solodovca† a Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia b Volgograd State Technical University, Volgograd, Russia c Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia Abstract: Holomorphic self-maps of the unit disc with two fixed diametrically opposite boundary points and an invariant diameter are investigated. Asymptotically sharp estimates for domains of univalence are obtained for functions in such classes, which depend on the product of the angular derivatives at the boundary fixed points. Bibliography: 16 titles. Keywords: holomorphic map, fixed points, angular derivative, domain of univalence.
† Author to whom correspondence should be addressed DOI: https://doi.org/10.4213/sm9367   Full text:
PDF file (586 kB)
 First page: PDF file
References:
PDF file
HTML file
English version: Sbornik: Mathematics, 2020, 211:11,
UDC: 517.54 MSC: 30C45, 30C55 Received: 30.12.2019 and 07.08.2020 Citation: O. S. Kudryavtseva, A. P. Solodov, “Asymptotically sharp two-sided estimate for domains of univalence of holomorphic self-maps of a disc with an invariant diameter”, Mat. Sb., 211:11 (2020), 
Citation in format AMSBIB
\Bibitem{KudSol20}Linking options:
Citing articles on Google Scholar: Russian citations, English citations Related articles on Google Scholar: Russian articles, English articles |
|
||||||||||||||||||||||||
|
|
Contact us: |
 Terms of Use
|
Registration |
Logotypes |
|