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Approximation of Conformal Mappings via Bieberbach Polynomials inside Regions with Cusps

Year 2019, Volume: 8 Issue: 4, 1288 - 1295, 24.12.2019
https://doi.org/10.17798/bitlisfen.641402

Abstract



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. 



References

  • 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.
Year 2019, Volume: 8 Issue: 4, 1288 - 1295, 24.12.2019
https://doi.org/10.17798/bitlisfen.641402

Abstract

References

  • 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.
There are 12 citations in total.

Details

Primary Language English
Journal Section Araştırma Makalesi
Authors

Cem Koşar 0000-0003-4949-4956

Publication Date December 24, 2019
Submission Date November 1, 2019
Acceptance Date November 25, 2019
Published in Issue Year 2019 Volume: 8 Issue: 4

Cite

IEEE C. Koşar, “Approximation of Conformal Mappings via Bieberbach Polynomials inside Regions with Cusps”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 8, no. 4, pp. 1288–1295, 2019, doi: 10.17798/bitlisfen.641402.

Bitlis Eren University
Journal of Science Editor
Bitlis Eren University Graduate Institute
Bes Minare Mah. Ahmet Eren Bulvari, Merkez Kampus, 13000 BITLIS