Bull. Korean Math. Soc. 2018; 55(1): 165-173
Online first article July 26, 2017 Printed January 31, 2018
https://doi.org/10.4134/BKMS.b160916
Copyright © The Korean Mathematical Society.
Halit Orhan, Pawe{\l} Zaprawa
Atat\"{u}rk University, Lublin University of Technology
In this paper we obtain the bounds of the third Hankel determinants for the classes $\mathcal{S}^\ast(\alpha)$ of starlike functions of order $\alpha$ and $\mathcal{K}(\alpha)$ of convex functions of order $\alpha$. Moreover,we derive the sharp bounds for functions in these classes which are additionally 2-fold or 3-fold symmetric.
Keywords: Hankel determinant, starlike functions, convex functions, $n$-fold symmetric functions
MSC numbers: 30C50
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