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ESTIMATES FOR A CERTAIN SUBCLASS OF HOLOMORPHIC FUNCTIONS

Ornek, Bulent Nafi;Akyel, Tugba

  • Received : 2017.10.16
  • Accepted : 2018.09.09
  • Published : 2019.05.31

Abstract

In this paper, a version of the boundary Schwarz Lemma for the holomorphic function belonging to $\mathcal{N}$(${\alpha}$) is investigated. For the function $f(z)=z+c_2z^2+C_3z^3+{\cdots}$ which is defined in the unit disc where $f(z){\in}\mathcal{N}({\alpha})$, we estimate the modulus of the angular derivative of the function f(z) at the boundary point b with $f(b)={\frac{1}{b}}\int\limits_0^b$ f(t)dt. The sharpness of these inequalities is also proved.

Keywords

holomorphic function;Jack's lemma;angular derivative