Hankel determinant of type $H_{2}(3)$ for inverse functions of some classes of univalent functions with missing second coefficient

TL;DR

This paper establishes upper bounds for the Hankel determinant of a specific type for inverse functions of certain univalent function classes, contributing to the understanding of their coefficient bounds.

Contribution

It provides new upper bounds for the Hankel determinant of type H_2(3) for inverse functions within specific univalent function classes.

Findings

Derived explicit upper bounds for |H_2(3)|

Applied bounds to inverse functions of univalent classes

Enhanced understanding of coefficient constraints in univalent functions

Abstract

In this paper we determine the upper bounds of $|H_{2}(3)|$ for the inverse functions of functions of some classes of univalent functions, where $H_{2}(3)(f)=a_{3}a_{5}-a_{4}^{2}$ is the Hankel determinant of a special type.