Journal of the
Korean Mathematical Society JKMS

The estimate of third Hankel determinant \begin{eqnarray*} H_{3,1}(f)=\;\vline \;\begin{matrix}{} a_1 & a_2 & a_3 \\ a_2 & a_3 & a_4 \\ a_3 & a_4 & a_5 \end{matrix} \;\vline\\ \end{eqnarray*} of the analytic function $f(z)=z+a_2z^2+a_3z^3+\cdots,$ for which $\Re(1+zf''(z)/f'(z))>-1/2$ are investigated. The corrected version of a known results \cite[Theorem 3.1 and Theorem 3.3]{babalola1} are also obtained.

Keywords: analytic functions, univalent function, close-to-convex functions, starlike functions, Fekete-Szeg\"{o} functional, Hankel determinant

MSC numbers: 30C45, 30C50