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GENERALIZATION OF THE JULIA–CARATHE´ODORY THEOREM TO THE CASE OF SEVERAL BOUNDARY FIXED POINTS
- Authors: Kudryavtseva O.S1,2
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Affiliations:
- Lomonosov Moscow State University, Moscow Center of Fundamental and Applied Mathematics
- Volgograd State Technical University
- Issue: Vol 522, No 1 (2025)
- Pages: 25-32
- Section: MATHEMATICS
- URL: https://jdigitaldiagnostics.com/2686-9543/article/view/683771
- DOI: https://doi.org/10.31857/S2686954325020059
- EDN: https://elibrary.ru/HYZQZS
- ID: 683771
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Abstract
Holomorphic self-maps of the unit disc with boundary fixed points are investigated. In 1982, Cowen and Pommerenke established an interesting generalization of the classical Julia— Carathe´odory theorem, which allowed them to derive an exact estimate for the derivative at the Denjoy—Wolff point on a class of functions with an arbitrary finite set of boundary fixed points. In this paper, we obtain a new generalization of the Julia—Carathe´odory theorem, which contains Cowen—Pommerenke result as a special case, moreover, it is an effective tool for solving various problems on classes of functions with fixed points.
About the authors
O. S Kudryavtseva
Lomonosov Moscow State University, Moscow Center of Fundamental and Applied Mathematics; Volgograd State Technical University
Email: kudryavceva_os@mail.ru
Moscow, Russia; Volgograd, Russia
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