Dissipative holomorphic functions, Bloch radii, and the Schwarz Lemma

2000 ◽  
Vol 82 (1) ◽  
pp. 221-232 ◽  
Author(s):  
Lawrence A. Harris ◽  
Simeon Reich ◽  
David Shoikhet
Keyword(s):  
Holomorphic Functions ◽  
Schwarz Lemma ◽  
The Schwarz Lemma

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

2019 ◽  
Vol 38 (7) ◽  
pp. 219-226
Author(s):  
Tugba Akyel ◽  
Bulent Nafi Ornek
Keyword(s):  
Boundary Point ◽  
Meromorphic Functions ◽  
Schwarz Lemma ◽  
Jack’S Lemma ◽  
Boundary Version ◽  
Jack's Lemma ◽  
The Schwarz Lemma

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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