Bulletin of the
Korean Mathematical Society BKMS

A normalized analytic function $f$ is parabolic starlike if $w(z)$ $:=zf'(z)/f(z)$ maps the unit disk into the parabolic region $\{w: \operatorname{Re} w>|w-1|\}$. Sharp estimates on the third Hermitian-Toeplitz determinant are obtained for parabolic starlike functions. In addition, upper bounds on the third Hankel determinants are also determined.

Keywords: Parabolic starlike functions, uniformly convex functions, Hankel determinant, Hermitian-Toeplitz determinant, subordination

MSC numbers: Primary 30C45, 30C50