Hankel determinant of second order for some classes of analytic functions

Abstract

Let $f$ be analytic in the unit disk $\mathbb{D}$ and normalized so that $f(z)=z+a_2{z}^2+a_3{z}^3+\cdots$. In this paper, we give upper bounds of the Hankel determinant of second order for the classes of starlike functions of order $\alpha$, Ozaki close-to-convex functions and two other classes of analytic functions. Some of the estimates are sharp.