Sharp bounds of Hankel determinants of second and third order for inverse functions of certain class of univalent functions

Abstract

Let $\mathcal{A}$ be the class of functions that are analytic in the unit disc $\mathbb{D}$, normalized such that $f(z)=z+{\sum }_{n=2}^{\infty }{a}_n{z}^n$, and let class $\mathcal{U}(\lambda )$, $0<\lambda \le 1$, consists of functions $f\in \mathcal{A}$, such that \[ \left |\left (\frac{z}{f(z)} \right )^{2}f'(z)-1\right | < λ\quad (z\in {\mathbb D}). \] In this paper we determine the sharp upper bounds for the Hankel determinants of second and third order for the inverse functions of functions from the class $\mathcal{U}(\lambda )$.