scholarly journals Uniqueness part of Schwarz lemma for driving point impedance functions

Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 2953-2959
Author(s):  
Nafi Örnek ◽  
Timur Düzenli
Keyword(s):  
Uniqueness Theorem ◽  
Schwarz Lemma ◽  
Boundary Points ◽  
Impedance Functions ◽  
Boundary Version ◽  
The Schwarz Lemma

In this paper, a boundary version of the uniqueness part of the Schwarz lemma for driving point impedance functions has been investigated. Also, more general results have been obtained for a different version of the Burns-Krantz uniqueness theorem. In these results, as different from the Burns-Krantz theorem, only the boundary points have been used as the conditions on the function. Also, more general majorants will be taken instead of power majorants in (1.1).

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.

scholarly journals Representation with majorant of the Schwarz lemma at the boundary

2017 ◽  
Vol 101 (115) ◽  
pp. 191-196
Author(s):  
Bülent Örnek ◽  
Tuğba Akyel
Keyword(s):  
Holomorphic Function ◽  
Blaschke Product ◽  
Unit Disc ◽  
Sufficient Conditions ◽  
Schwarz Lemma ◽  
Local Behavior ◽  
Finite Blaschke Product ◽  
Boundary Points ◽  
Finite Set ◽  
The Schwarz Lemma

Let f be a holomorphic function in the unit disc and |f(z)?1| < 1 for |z| < 1. We generalize the uniqueness portion of Schwarz?s lemma and provide sufficient conditions on the local behavior of f near a finite set of boundary points that needed for f to be a finite Blaschke product.

scholarly journals New estimates for meromorphic functions

2021 ◽  
Vol 109 (123) ◽  
pp. 153-162
Author(s):  
Bülent Örnek
Keyword(s):  
Boundary Point ◽  
Unit Disc ◽  
Meromorphic Functions ◽  
Schwarz Lemma ◽  
Angular Derivative ◽  
Boundary Version ◽  
The Schwarz Lemma

A boundary version of the Schwarz lemma for meromorphic functions is investigated. For the function Inf(z) = 1/z +?? k=2 knck?2zk?2, belonging to the class of W, we estimate from below the modulus of the angular derivative of the function on the boundary point of the unit disc.

scholarly journals Uniqueness part of the Schwarz lemma at the boundary

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3643-3650
Author(s):  
Bülent Örnek ◽  
Tuğba Akyel
Keyword(s):  
Schwarz Lemma ◽  
Inner Functions ◽  
Boundary Version ◽  
The Schwarz Lemma

In this paper, a boundary version of the uniqueness (or, rigidity) part of the Schwarz lemma should be investigated. Also, new results related to inner functions, inner capacities, and bilogaritmic concave majorants are obtained.

scholarly journals Behavior of meromorphic functions at the boundary of the unit disc

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3443-3452
Author(s):  
Bülent Örnek
Keyword(s):  
Meromorphic Function ◽  
Boundary Point ◽  
Unit Disc ◽  
Meromorphic Functions ◽  
Schwarz Lemma ◽  
Angular Derivative ◽  
Boundary Version ◽  
The Schwarz Lemma

In this paper, a boundary version of the Schwarz lemma for meromorphic functions is investigated. The modulus of the angular derivative of the meromorphic function Inf(z)=1/z+2nc0+3nc1z+4nc2z2+... that belongs to the class of M on the boundary point of the unit disc has been estimated from below.

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