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Some estimates for angular derivative at the boundary
Authors: Bülent Nafi Örnek
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Abstract
In this paper, we establish lower estimates for the modulus of the values of $f(z)$ on boundary of unit disc. For the function $f(z)=1+c_{1}z+c_{2}z^{2}+...$ defined in the unit disc such that $f(z)\in \mathcal{N}\left( \beta \right) $ assuming the existence of angular limit at the boundary point $b$, the estimations below of the modulus of angular derivative have been obtained at the boundary point $b$ with $f(b)=\beta $. Moreover, Schwarz lemma for class $\mathcal{N}\left( \beta \right) $ is given. The sharpness of these inequalities has been proved.Department of Computer Engineering
Amasya University
Merkez-Amasya 05100, Turkey
E-mail: ,
Amasya University
Merkez-Amasya 05100, Turkey
E-mail: ,
Fulltext
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Contents
- Semi-symmetric isotopic closure of some group varieties and the corresponding identities
- Factorizations in the rings of the block matrices
- Inclusion Properties of Certain Subclass of Univalent Meromorphic Functions Defined by a Linear Operator Associated with the $\lambda$-Generalized Hurwitz-Lerch Zeta Function
- Interpolating Bézier spline surfaces with local control
- A Note on the Equivalence of Control Systems on Lie Groups
- Viscous flow through a porous medium filled by liquid with varying viscosity
- Invariant conditions of stability of unperturbed motion governed by some differential systems in the plane
- A Note on 2-Hypersurfaces of the Nearly Kählerian Six-Sphere
- Post-quantum No-key Protocol
- Some estimates for angular derivative at the boundary
