Hankel Determinants of Normalized Analytic Functions Associated with Hyperbolic Secant Function

Kumar S., Breaz D., Cotirla L., Cetinkaya A.

SYMMETRY-BASEL, vol.16, no.10, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 10
  • Publication Date: 2024
  • Doi Number: 10.3390/sym16101303
  • Journal Name: SYMMETRY-BASEL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Istanbul Kültür University Affiliated: Yes

Abstract

In this paper, we consider a subclass of normalized analytic functions associated with the hyperbolic secant function. We compute the sharp bounds on third- and fourth-order Hermitian-Toeplitz determinants for functions in this class. Moreover, we determine the bounds on second- and third-order Hankel determinants, as well as on the generalized Zalcman conjecture. We examine a Briot-Bouquet-type differential subordination involving the Bernardi integral operator. Finally, we obtain a univalent solution to the Briot-Bouquet differential equation, and discuss the majorization property for such function classes.