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Radii Problems for Starlike Functions and Semigroup Generators

Abstract

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.

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Acknowledgements

The authors are very grateful to the anonym referee whose recommendations essentially improved the content of the paper.

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Correspondence to Nikola Tuneski.

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Communicated by Dmitry Khavinson.

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Elin, M., Shoikhet, D. & Tuneski, N. Radii Problems for Starlike Functions and Semigroup Generators. Comput. Methods Funct. Theory 20, 297–318 (2020). https://doi.org/10.1007/s40315-020-00311-2

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Keywords

  • Holomorphic generators
  • Starlike functions
  • One-parameter semigroups

Mathematics Subject Classification

  • 30C45
  • 47H20
  • 30C80
  • 37L05