# Hankel determinant of second order for some classes of analytic functions

## TL;DR

This paper establishes upper bounds for the second-order Hankel determinant in various classes of analytic functions, including starlike and close-to-convex functions, with some bounds proven to be sharp.

## Contribution

It provides new upper bounds for the second-order Hankel determinant for specific classes of analytic functions, some of which are sharp, advancing understanding in geometric function theory.

## Key findings

- Derived upper bounds for the Hankel determinant of second order.
- Identified sharp bounds for certain classes of functions.
- Extended results to multiple classes of analytic functions.

## Abstract

Let $f$ be analytic in the unit disk $\mathbb D$ and normalized so that $f(z)=z+a_2z^2+a_3z^3+\cdots$. 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.