An Extremal Problem for Odd Univalent Polynomials

Dmitriy Dmitrishin, Daniel Gray, Alexander Stokolos, Iryna Tarasenko

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

For the univalent polynomials F(z)=∑j=1Najz2j-1 with real coefficients and normalization a1=1 we solve the extremal problem (Formula presented.) We show that the solution is (Formula presented.) and the extremal polynomial (Formula presented.) is unique and univalent, where Uj(x) is a Chebyshev polynomial of the second kind and Uj(x) denotes the derivative. As an application, we obtain an estimate of the Koebe radius for odd univalent polynomials in D and formulate several conjectures.

Original languageEnglish
Pages (from-to)83-100
Number of pages18
JournalComputational Methods and Function Theory
Volume24
Issue number1
DOIs
StatePublished - Mar 2024

Keywords

  • Chebyshev polynomials
  • Koebe one-quarter theorem
  • Odd univalent polynomials
  • T-folded Koebe function

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