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## Some estimates for angular derivative at the boundary

Authors: Bülent Nafi Örnek

### Abstract

In this paper, we establish lower estimates for the modulus of the values of $f(z)$ on boundary of unit disc. For the function $f(z)=1+c_{1}z+c_{2}z^{2}+...$ defined in the unit disc such that $f(z)\in \mathcal{N}\left( \beta \right)$ assuming the existence of angular limit at the boundary point $b$, the estimations below of the modulus of angular derivative have been obtained at the boundary point $b$ with $f(b)=\beta$. Moreover, Schwarz lemma for class $\mathcal{N}\left( \beta \right)$ is given. The sharpness of these inequalities has been proved.

Department of Computer Engineering
Amasya University
Merkez-Amasya 05100, Turkey
E-mail: ,

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