Symmetrization of Suffridge polynomials and approximation of T-symmetric Koebe functions

Dmitriy Dmitrishin, Andrey Smorodin, Alex Stokolos, Mihai Tohaneanu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The article studies extremal properties of certain T-symmetric polynomials, which generalize the famous Suffridge polynomials. Our first result establishes an asymptotic estimate for the maximum modulus in the unit disk. Our second result uses these polynomials to approximate univalent functions in the unit disk, which is the analogue of the Andrievskii-Ruscheweych subordination [1] to T-symmetric polynomials. The main technical tool is a limit formula for representing an exponential function as a product of trigonometric functions.

Original languageEnglish
Article number125350
JournalJournal of Mathematical Analysis and Applications
Volume503
Issue number2
DOIs
StatePublished - Nov 15 2021

Bibliographical note

Funding Information:
M.T. is partially supported by a grant from the Simons Foundation (# 586051 ).

Publisher Copyright:
© 2021 Elsevier Inc.

Keywords

  • Suffridge polynomials
  • T-symmetric Koebe function
  • T-symmetric univalent polynomials

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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