THE THIRD HANKEL DETERMINANT FOR INVERSE COEFFICIENTS OF CONVEX FUNCTIONS

Abstract Let $\mathcal {A}$ denote the class of normalised analytic functions f in the open unit disk $\mathbb {D}:=\{z\in \mathbb {C}:|z|<1\}$ with $f(0)=0$ and $f'(0)=1$ . A function $f\in \mathcal {A}$ is said to be convex if $f(\mathbb {D})$ is convex. We establish a sharp upper bound for the third Hankel determinant corresponding to the inverse coefficients of convex univalent (that is, one-to-one) functions in the unit disk $\mathbb {D}$ .