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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-Szego 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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참고문헌 (19)
참고문헌 신청
T. Akyel / 2016 / Sharpened forms of the Generalized Schwarz inequality on the boundary / Proc. Indian Acad. Sci. (Math. Sci.) 126(1):69~78
T. A. Azeroglu / 2013 / A refined Schwarz inequality on the boundary / Complex Variab. Elliptic Equa 58:571~577
H. P. Boas / 2010 / Julius and Julia : Mastering the Art of the Schwarz lemma / Amer. Math. Monthly 117:770~785
V. N. Dubinin / 2004 / The Schwarz inequality on the boundary for functions regular in the disc / J. Math. Sci 122:3623~3629
G. M. Golusin / 1966 / Geometric Theory of Functions of Complex Variable [in Russian]
T. A. Azeroglu / 2013 / A refined Schwarz inequality on the boundary / Complex Variab. Elliptic Equa 58:571~577
H. P. Boas / 2010 / Julius and Julia : Mastering the Art of the Schwarz lemma / Amer. Math. Monthly 117:770~785
V. N. Dubinin / 2004 / The Schwarz inequality on the boundary for functions regular in the disc / J. Math. Sci 122:3623~3629
G. M. Golusin / 1966 / Geometric Theory of Functions of Complex Variable [in Russian]
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