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Izv. Akad. Nauk SSSR Ser. Mat., 1978, Volume 42, Issue 4, Pages 870–878 (Mi izv1850)  

This article is cited in 13 scientific papers (total in 13 papers)

On the convergence of Bieberbach polynomials in the case of a Lipschitz domain

I. B. Simonenko


Abstract: Uniform convergence of the Bieberbach polynomials is proved in the case of a simply connected region bounded by a Lipschitz Jordan curve.
Bibliography: 11 titles.

Full text: PDF file (699 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1979, 13:1, 166–174

Bibliographic databases:

UDC: 517.52
MSC: 30C10, 30C70
Received: 17.05.1976

Citation: I. B. Simonenko, “On the convergence of Bieberbach polynomials in the case of a Lipschitz domain”, Izv. Akad. Nauk SSSR Ser. Mat., 42:4 (1978), 870–878; Math. USSR-Izv., 13:1 (1979), 166–174

Citation in format AMSBIB
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\by I.~B.~Simonenko
\paper On the convergence of Bieberbach polynomials in the case of a~Lipschitz domain
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1978
\vol 42
\issue 4
\pages 870--878
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=508831}
\zmath{https://zbmath.org/?q=an:0425.30032|0383.30024}
\transl
\jour Math. USSR-Izv.
\yr 1979
\vol 13
\issue 1
\pages 166--174
\crossref{https://doi.org/10.1070/IM1979v013n01ABEH002017}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. V. Kulikov, “$L_p$-convergence of Bieberbach polynomials”, Math. USSR-Izv., 15:2 (1980), 349–371  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. I. V. Kulikov, “$W_2^1$$L_\infty$-convergence of Bieberbach polynomials in a Lipschitz domain”, Russian Math. Surveys, 36:5 (1981), 161–162  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. N. Papamichael, M. K. Warby, “Stability and convergence properties of Bergman kernel methods for numerical conformal mapping”, Numer Math, 48:6 (1986), 639  crossref  mathscinet  zmath  isi
    4. Dieter Gaier, “On the convergence of the Bieberbach polynomials in regions with corners”, Constr Approx, 4:1 (1988), 289  crossref  mathscinet  zmath  isi
    5. N Papamichael, E.B Saff, “Local behaviour of the error in the Bergman kernel method for numerical conformal mapping”, Journal of Computational and Applied Mathematics, 46:1-2 (1993), 65  crossref
    6. V. V. Andrievskii, I. E. Pritsker, “Convergence of Bieberbach polynomials in domains with interior cusps”, J Anal Math, 82:1 (2000), 315  crossref  mathscinet  zmath  isi
    7. Daniyal M. Israfilov, “Uniform convergence of the Bieberbach polynomials in closed smooth domains of bounded boundary rotation”, Journal of Approximation Theory, 125:1 (2003), 116  crossref
    8. Nicolas Papamichael, “Dieter Gaier’s Contributions to Numerical Conformal Mapping”, Comput. Methods Funct. Theory, 3:1 (2004), 1  crossref
    9. M. Kucukaslan, C. Koşar, F. G. Abdullayev, “Uniform Convergence of Some Extremal Polynomials in Domain with Corners on the Boundary”, J Inequal Appl, 2010 (2010), 1  crossref
    10. Burcin Oktay, Daniyal M. Israfilov, “An approximation of conformal mappings on smooth domains”, Complex Variables and Elliptic Equations, 2011, 1  crossref
    11. F.G.. Abdullayev, Cem Koşar, Mehmet Kucukaslan, “Uniform Convergence of Extremal Polynomials When Domains Have Corners and Special Cusps on the Boundary”, APM, 01:06 (2011), 305  crossref
    12. F. G. Abdullayev, N. P. Ö zkartepe, “On the improvement of the rate of convergence of the generalized Bieberbach polynomials in domains with zero angles”, Ukr Math J, 2012  crossref
    13. F.G.. Abdullayev, P.N.. Özkartepe, “Uniform convergence of the p-Bieberbach polynomials in domains with zero angles”, Sci. China Math, 2014  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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