Radii Problems for Starlike Functions and Semigroup Generators

In this paper, we discover new connections between topics in classical geometric function theory and complex dynamics. In particular, we study some classes of starlike functions and their embeddings in the classes of semigroup generators. In addition, we find explicit formulas for the radii of starl...

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Bibliographic Details
Published in:Computational methods and function theory 2020-06, Vol.20 (2), p.297-318
Main Authors: Elin, Mark, Shoikhet, David, Tuneski, Nikola
Format: Article
Language:English
Subjects:
Analysis
Computational Mathematics and Numerical Analysis
Functions of a Complex Variable
Generators
Mathematics
Mathematics and Statistics
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Summary:In this paper, we discover new connections between topics in classical geometric function theory and complex dynamics. In particular, we study some classes of starlike functions and their embeddings in the classes of semigroup generators. In addition, we find explicit formulas for the radii of starlikeness for those classes and uniform rates of convergence of semigroups to their Denjoy–Wolff points.
ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-020-00311-2