Bulletin of the
Korean Mathematical Society BKMS

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