Symmetry (Sep 2024)

Upper Bounds of the Third Hankel Determinant for Bi-Univalent Functions in Crescent-Shaped Domains

  • Qasim Ali Shakir,
  • Adel Salim Tayyah,
  • Daniel Breaz,
  • Luminita-Ioana Cotîrlă,
  • Eleonora Rapeanu,
  • Fethiye Müge Sakar

DOI
https://doi.org/10.3390/sym16101281
Journal volume & issue
Vol. 16, no. 10
p. 1281

Abstract

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This paper investigates the third Hankel determinant, denoted H3(1), for functions within the subclass RS∑*(λ) of bi-univalent functions associated with crescent-shaped regions φ⦅z=z+1+z2. The primary aim of this study is to establish upper bounds for H3(1). By analyzing functions within this specific geometric context, we derive precise constraints on the determinant, thereby enhancing our understanding of its behavior. Our results and examples provide valuable insights into the properties of bi-univalent functions in crescent-shaped domains and contribute to the broader theory of analytic functions.

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