The third Hankel determinant for inverse coefficients of starlike functions of order 1/2

TL;DR

This paper establishes the exact bound for the third Hankel determinant of inverse coefficients of starlike functions of order 1/2, revealing invariance properties within this function class.

Contribution

It provides the sharp bound for the third Hankel determinant for inverse coefficients of starlike functions of order 1/2, a novel result in geometric function theory.

Findings

Sharp bound for the third Hankel determinant of inverse coefficients

Invariance of certain functionals on the class ^*(1/2)

Enhanced understanding of coefficient bounds for starlike functions

Abstract

The sharp bound for the third Hankel determinant for the coefficients of the inverse function of starlike function of order $1/2$ is obtained. In light of this, we can deduce that the functionals $|H_3(1)(f)|$ and $|H_3(1)(f^{-1})|$ exhibit invariance on the class $\mathcal{S}^*(1/2)$.