The Sharp Bounds of the Third-Order Hankel Determinant of Inverse Functions for Certain Univalent Functions

This paper investigates the precise upper bound of the third-order Hankel determinant for the inverse functions within the function classes $\mathcal S^{*}_{e}$, $\mathcal C_{e}$, $\mathcal S^{*}_{\mathcal L}$, and $\mathcal C_{\mathcal L}$. Additionally, it establishes the upper bound for the second-order Hankel determinant of the logarithmic coefficient in function class $\mathcal S^{*}_{\mathcal L}$, as well as the third-order Hankel determinant for function class $\mathcal C_{car}$.