Hankel determinant for a class of analytic functions
Date Issued
2019-03-19
Author(s)
Milutin Obradovic
Nikola Tuneski
Abstract
Let $f$ be analutic in the unit disk $\mathbb D$ and normalized so that
$f(z)=z+a_2z^2+a_3z^3+\cdots$. In this paper we give sharp bound of Hankel
determinant of the second order for the class of analytic unctions satisfying
\[ \left|\arg \left[\left(\frac{z}{f(z)}\right)^{1+\alpha}f'(z) \right]
\right|<\gamma\frac{\pi}{2} \quad\quad (z\in\mathbb D),\] for $0<\alpha<1$ and
$0<\gamma\leq1$.
$f(z)=z+a_2z^2+a_3z^3+\cdots$. In this paper we give sharp bound of Hankel
determinant of the second order for the class of analytic unctions satisfying
\[ \left|\arg \left[\left(\frac{z}{f(z)}\right)^{1+\alpha}f'(z) \right]
\right|<\gamma\frac{\pi}{2} \quad\quad (z\in\mathbb D),\] for $0<\alpha<1$ and
$0<\gamma\leq1$.