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Dergiler / 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
Sayfa
209–216
Yayın Tarihi
2022-10-18
DOI
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The approximation rate in dependence of the smoothness parameters of the considered domains is estimated.

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Amaç & Hipotez: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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Temel Bulgular & Veri:In this work the simultaneous approximations of $\varphi_0$ and its derivatives by Bieberbach polynomials are investigated.
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Sonuç & Katkı:The approximation rate in dependence of the smoothness parameters of the considered domains is estimated.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (18)

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