Some lower bound for holomorphic functions at the boundary

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Authors :

Bülent NafiÖrnek1*

Author Address :

1Department of Computer Engineering, Amasya University, Merkez-Amasya 05100, Turkey.

*Corresponding author.

Abstract :

In this paper, a boundary version of the Schwarz lemma for classes $mathcal{%H(alpha )}$ is investigated. For the function $f(z)=1+c_{1}z+c_{2}z^{2}+...$defined in the unit disc such that $f(z)in mathcal{H(alpha )}$ $left(0<alpha leq 1 ight) $, we estimate a modulus of the angular derivative of $f(z)$ function at the boundary point $b$ with $f(b)=e^{frac{pi alpha }{2}%}$. The sharpness of these inequalities is also proved.

Keywords :

Holomorphic function, Jack’s lemma, Angular derivative.

DOI :

10.26637/MJM0601/0019

Article Info :

Received : September 17, 2017; Accepted : December 12, 2017.

 

 

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