Approximation of Conformal Mappings via Bieberbach Polynomials inside Regions with Cusps

Yıl 2019, Cilt: 8 Sayı: 4, 1288 - 1295, 24.12.2019

Cem Koşar

https://doi.org/10.17798/bitlisfen.641402

Öz

Bu çalışmada, kompleks düzlemin;
sonlu, basit bağlantılı ve aynı zamanda hem iç sıfır açı hem de dış sıfır açıya
sahip bölgelerin içerisinde konform dönüşümlere
Bieberbach polinomlarıyla yaklaşımı için bazı hesaplamalar elde edimiştir.
Ayrıca yaklaşımın hızı bölgenin geometrik özelliğine bağlıdır. 

Anahtar Kelimeler

Conformal mapping, Bieberbach polynomials, quasiconformal curve

Kaynakça

• Referans1. Abdullayev F.G. 1986. On the orthogonal polynomials in domains with quasiconformal boundary (Russian), Dissertation, Donetsk.
• Referans2. Abdullayev F.G., Baki A. 2001. On the convergence of Bieberbach polynomials in domains with interior zero angles, Complex Variables Theor. Appl., 44 (2): 131-144.
• Referans3. Abdullayev F.G. 1989. On the convergence of Fourier series by orthogonal polynomials in domains with piecewise-quasiconformal boundary, Theory of Mapping and Approx., Kiev, Naukova Dumka, 3-12.
• Referans4. Abdullayev F.G. 1997. Uniform convergence of the generalized Bieberbach polynomials in regions with non-zero angles, Acta Math. Hung., 77(3): 223-246.
• Referans5. Abdullayev F.G. 2001. Uniform convergence of the generalized Bieberbach polynomials in regions with zero angles, Czechoslovak Math. J., 51(126): 643-660.
• Referans6. Abdullayev F.G. 2001. Uniform convergence of the Bieberbach polynomials inside and on the closure of domain in the complex plane, East J. Approx., 7(1):77-101.
• Referans7. Abdullayev F.G. 2018. Uniform convergence of the generalized Bieberbach polynomials in regions with simultaneously exterior and interior zero angles, Complex Analysis and Operator Theory, https://doi.org/10.1007/s-11785-018-0857-7.
• Referans8. Ahlfors L.V. 1966. Lectures on Quasiconformal Mappings, Van Nostrand, Princeton.
• Referans9. Andrievskii V.V. 1983. Uniform convergence of Bieberbach polynomials in domains with piecewise-quasiconformal boundary, (Russian), Theory of Mapping and Approx. Functions, Kiev, Naukova Dumka: 3-18.
• Referans10. Andrievskii V.V. 1983. Convergence of Bieberbach polynomials in domains with quasicon- formal boundary, Ukr. Math. J., 35: 233-236.
• Referans11. Gaier D. 1988. On the convergence of Bieberbach polynomials in regions with corners, Const. Approx. 4, 289-305.
• Referans12. Gaier D. 1994. Polynomial approximation of conformal maps, Const. Approx. 14, 27-40.