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 inComputational methods and function theory Vol. 20; no. 2; pp. 297 - 318
Main Authors Elin, Mark, Shoikhet, David, Tuneski, Nikola
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2020
Springer Nature B.V
Subjects
Analysis
Computational Mathematics and Numerical Analysis
Functions of a Complex Variable
Generators
Mathematics
Mathematics and Statistics
Starlike functions
30C45
47H20
37L05
One-parameter semigroups
30C80
Holomorphic generators
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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