An improvement of the estimates of the modulus of the Hankel determinants of second and third order for the class $\mathcal{S}$ of univalent functions

TL;DR

This paper enhances the bounds on the Hankel determinants of second and third order for univalent functions by leveraging properties of Grunsky coefficients, advancing previous estimates.

Contribution

It introduces improved upper bounds for Hankel determinants of second and third order for the class of univalent functions using Grunsky coefficients.

Findings

Tighter upper bounds for second and third order Hankel determinants.

Application of Grunsky coefficients to improve estimates.

Advancement over previous bounds in the literature.

Abstract

Using some properties of the Grunsky coefficients we improve earlier results for upper bounds of the Hankel determinants of the second and third order for the class $\mathcal{S}$ of univalent functions.