No abstract

We study the sharp bound for the third Hankel determinant for the inverse function $f$, when it belongs to of the class of starlike functions with respect to symmetric points.Let $\mathcal{S}^{\ast}_{s}$ be the class of starlike functions with respect to symmetric points. In the article proves the following statements (Theorem): If $f\in \mathcal{S}^{\ast}_{s}$ then\begin{equation*}\big|H_{3,1}(f^{-1})\big|\leq1,\end{equation*}and the result is sharp for $f(z)=z/(1-z^2).$

The objective of this paper is to estimate the best possible upper bound to the third Hankel determinant for the inverse of functions with normalized conditions f (0) = 0, f ′(0) = 1 in the unit disc whose derivative has positive real part.

We present the sharp bounds for the third Hankel determinant [Formula: see text] and Zalcman functional [Formula: see text] of the inverse function of the familiar subfamily of starlike functions associated with the right half of lemniscate of Bernoulli.

The objective of this paper is to estimate the sharp bound of thethird Hankel determinant for kth- root transformation to the familiar subfamilyof starlike functions associated with the right half of lemniscate of Bernoulli. 2020 Mathematics Subject Classification. 30C45, 30C50.