Geodesic
Some Results Concerned with Hankel Determinant
Kragujevac Journal of Mathematics, Tome 47 (2023) no. 3, p. 481 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

In this paper, we discuss different versions of the boundary Schwarz lemma and Hankel determinant for $\mathcal{K}\left( \alpha \right) $ class. Also, for the function $f(z)=z+c_{2}z^{2}+c_{3}z^{3}+\cdots$ defined in the unit disc such that $f\in \mathcal{K(\alpha )}$, we estimate a modulus of the angular derivative of $f(z)$ function at the boundary point $z_{0}$ with $f(z_{0})=\frac{z_{0}}{1+\alpha }$ and $f^{\prime }(z_{0})=\frac{1}{1+\alpha }$. That is, we shall give an estimate below $\left\vert f^{\prime \prime }(z_{0})\right\vert $ according to the first nonzero Taylor coefficient of about two zeros, namely $z=0$ and $z_{1}\neq 0$. The sharpness of this inequality is also proved.
Classification : 30C80 32A10
Keywords: Fekete-Szegö functional, Julia-Wolff lemma, Hankel determinant, analytic function, Schwarz lemma angular derivative 
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Bülent Nafi Örnek. Some Results Concerned with Hankel Determinant. Kragujevac Journal of Mathematics, Tome 47 (2023) no. 3, p. 481 . http://geodesic.mathdoc.fr/item/KJM_2023_47_3_a10/