Applications of the Jack's lemma for the meromorphic functions at the boundary

  • Tugba Akyel Maltepe University
  • Bulent Nafi Ornek Amasya University

Abstract

In this paper, a boundary version of the Schwarz lemma for the class $\mathcal{% N(\alpha )}$ is investigated. For the function $f(z)=\frac{1}{z}% +a_{0}+a_{1}z+a_{2}z^{2}+...$ defined in the punctured disc $E$ such that $% f(z)\in \mathcal{N(\alpha )}$, we estimate a modulus of the angular derivative of the function $\frac{zf^{\prime }(z)}{f(z)}$ at the boundary point $c$ with $\frac{cf^{\prime }(c)}{f(c)}=\frac{1-2\beta }{\beta }$. Moreover, Schwarz lemma for class $\mathcal{N(\alpha )}$ is given.

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Author Biographies

Tugba Akyel, Maltepe University

The Faculty of Engineering and Natural Sciences

Bulent Nafi Ornek, Amasya University

Department of Computer Engineering

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Published
2019-10-14