Korean J. Math. Vol. 28 No. 4 (2020) pp.699-715
DOI: https://doi.org/10.11568/kjm.2020.28.4.699

Bounds of Hankel determinants for analytic function

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Published: Dec 30, 2020
Keywords:
Fekete-Szegö functional, Hankel determinant, Jack’s lemma, Analytic function, Schwarz lemma.
Mathematics Subject Classification:
Fekete-Szegö functional, 30C80, Jack’s lemma, 32A10

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Bülent Nafi Örnek
Department of Computer Engineering, Amasya University Merkez-Amasya, 05100, Turkey

Abstract

In this paper, we give estimates of the Hankel determinant $H_{2}(1)$ in a novel class $\mathcal{N}\left( \varepsilon \right) $ of analytical functions in the unit disc. In addition, the relation between the Fekete-Szegö function $H_{2}(1)$ and the module of the angular derivative of the analytical function $p(z)$ at a boundary point $b$ of the unit disk will be given. In this association, the coefficients in the Hankel determinant $b_{2}$, $b_{3}$ and $b_{4}$ will be taken into consideration. Moreover, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.


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