Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2023; 60(2): 281-291

Online first article March 21, 2023      Printed March 31, 2023

https://doi.org/10.4134/BKMS.b210368

Copyright © The Korean Mathematical Society.

The third Hermitian-Toeplitz and Hankel determinants for parabolic starlike functions

Rosihan M. Ali, Sushil Kumar, Vaithiyanathan Ravichandran

Universiti Sains Malaysia; Bharati Vidyapeeth's College of Engineering; National Institute of Technology

Abstract

A normalized analytic function $f$ is parabolic starlike if $w(z)$ $:=zf'(z)/f(z)$ maps the unit disk into the parabolic region $\{w: \operatorname{Re} w>|w-1|\}$. Sharp estimates on the third Hermitian-Toeplitz determinant are obtained for parabolic starlike functions. In addition, upper bounds on the third Hankel determinants are also determined.

Keywords: Parabolic starlike functions, uniformly convex functions, Hankel determinant, Hermitian-Toeplitz determinant, subordination

MSC numbers: Primary 30C45, 30C50