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.
Rosihan M. Ali, Sushil Kumar, Vaithiyanathan Ravichandran
Universiti Sains Malaysia; Bharati Vidyapeeth's College of Engineering; National Institute of Technology
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
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