The Second Hankel Determinant for Some Classes of Univalent Functions

Let \(\mathcal {S}\) $\mathcal{S}$ be the class of all analytic and univalent functions \(f(z)= z+\sum _{n=2}^{\infty }a_n z^n\) $f(z)=z+{\sum }_{n=2}^{\infty }{a}_n{z}^n$ in the unit disk \(\mathbb {D}=\{z\in \mathbb {C}:|z|<1\}\) $\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}$ . In this paper, we obtain sharp estimate of second-order Hankel determinants whose entries are Taylor coefficients, logarithmic coefficients, inverse coefficients and inverse logarithmic coefficients of f respectively for some subclasses of the class \(\mathcal {S}\) $\mathcal{S}$ .