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

Bülent Nafi Örnek

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.

Keywords


Fekete-Szegö functional, Hankel determinant, Jack’s lemma, Analytic function, Schwarz lemma.

Subject classification

30C80, 32A10

Sponsor(s)



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