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 SOME RESULTS CONCERNED WITH HANKEL DETERMINANT FOR N(α) CLASS Commun. Korean Math. Soc.Published online May 13, 2021 Bülent Nafi ÖRNEK and Gizem ATLI Amasya University Abstract : In this paper, we give some results an upper bounds of Hankel determinant of $H_{2}(1)$ for the classes of $N\left( \alpha \right) =\left( \frac{z}{f(z)}% \right) ^{2}f^{\prime }(z)-\alpha$, $\alpha \in %TCIMACRO{\U{2102} }% %BeginExpansion \mathbb{C} %EndExpansion$. We get a sharp upper bound for $H_{2}(1)=c_{3}-c_{2}^{2}$ for $\mathcal{N}% \left( \mathcal{\alpha }\right)$ by adding $z_{1},z_{2},...,z_{n}$ zeros of $f(z)$ which are different than zero. 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. Finally, the sharpness of the inequalities obtained in the presented theorems are proved. Keywords : Fekete-Szeg\"{o} functional, Julia-Wolff lemma, Hankel determinant, Analytic function, Schwarz lemma. Angular derivative. MSC numbers : 30C80, 32A10 Full-Text :