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Journals / Hacettepe Journal of Mathematics and Statistics / 2017 / Cilt: 46 - Sayı: 2

Simultaneous approximation of the Riemann conformal map and its derivatives by Bieberbach polynomials

Daniyal M. ISRAFİLOV
Pages
209–216
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The approximation rate in dependence of the smoothness parameters of the considered domains is estimated.

📌 3 Key Takeaways

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Objective & Hypothesis:Let $G$ be a domain in the complex plane $\mathbb{C}$ bounded by a rectifiable Jordan curve $\Gamma$, let $z_0\in G$ and let $\varphi_0$ be the Riemann conformal map of $G$ onto $\mathbb{D}_r:=\{ w\in\mathbb{C}\,:\, |w|<r \}$, normalized by $\varphi_0(z_0)=0$, $\varphi_0'(z_0)=1$.
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Key Findings & Data:In this work the simultaneous approximations of $\varphi_0$ and its derivatives by Bieberbach polynomials are investigated.
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Conclusion & Impact:The approximation rate in dependence of the smoothness parameters of the considered domains is estimated.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Bieberbach polynomials · conformal map · simultaneous approximation

Abstract

Let $G$ be a domain in the complex plane $\mathbb{C}$ bounded by a rectifiable Jordan curve $\Gamma$, let $z_0\in G$ and let $\varphi_0$ be the Riemann conformal map of $G$ onto $\mathbb{D}_r:=\{ w\in\mathbb{C}\,:\, |w|<r \}$, normalized by $\varphi_0(z_0)=0$, $\varphi_0'(z_0)=1$. In this work the simultaneous approximations of $\varphi_0$ and its derivatives by Bieberbach polynomials are investigated. The approximation rate in dependence of the smoothness parameters of the considered domains is estimated.

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Cite This Article

ISRAFİLOV, D. M. (2022). Simultaneous approximation of the Riemann conformal map and its derivatives by Bieberbach polynomials. Hacettepe Journal of Mathematics and Statistics, Cilt: 46 - Sayı: 2, 209–216. https://ajindex.com/articles/530017

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