Bulletin of the
Korean Mathematical Society BKMS

We prove sharp bounds for Hankel determinants for starlike functions $f$ with respect to symmetrical points, i.e., $f$ given by $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$ for $z\in \mathbb{D}$ satisfying $$ Re\dfrac{zf'(z)}{f(z)-f(-z)}>0, \quad z\in \mathbb{D}. $$ We also give sharp upper and lower bounds when the coefficients of $f$ are real.

Keywords: Starlike functions, close-to-convex functions, Hankel determinant, coefficient problems

MSC numbers: Primary 30C45

Supported by: The authors would like to express their thanks to the referees for their valuable comments and suggestions. The first named author (N. E. Cho) was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2019R1I1A3A01050861).