Hermitian Toepliz determinants for the class $\mathcal{S}$ of univalent functions

TL;DR

This paper introduces a novel method to accurately estimate third-order Hermitian Toepliz determinants for univalent functions in the unit disc, with applications to subclasses of these functions.

Contribution

The paper presents a new approach for estimating Hermitian Toepliz determinants, providing sharp bounds for the class of univalent functions and its subclasses.

Findings

Sharp estimates of third-order Hermitian Toepliz determinants for class  of univalent functions.

Method applicable to subclasses of  with illustrative examples.

Enhanced understanding of determinant bounds in geometric function theory.

Abstract

Introducing a new method we give sharp estimates of the Hermitian Toepliz determinants of third order for the class $\mathcal{S}$ of functions univalent in the unit disc. The new approach is also illustrated on some subclasses of the class $\mathcal{S}$.