Skip to main content
SpringerLink
Log in

Approximation of continuous periodic functions of one or two variables by Rogozinski polynomials of interpolation type

  • Brief Communications
  • Published:
Ukrainian Mathematical Journal Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literature cited

  1. W. Rogozinski, Über die Abschnitte trigonometrischer Reihen, Mathematische Annalen,95 (1926).

  2. N. P. Korneichuk, “Approximation of periodic functions satisfying a Lipschitz condition by Bernshtein-Rogozinski sums,” Dokl. Akad. Nauk SSSR,125, No.2 (1959).

  3. V. K. Dzyadyk and A. I. Stepanets, “Asymptotic equalities for least upper bounds of approximations of functions of a Holder class by Rogozinski polynomials,” Ukr. Matem. Zh.,24, No. 4 (1972).

  4. S. N. Bernshtein, “Trigonometric interpolation by means of least squares,” Dokl. Akad. Nauk SSSR,4 (1934) (also see Collected Works [in Russian], Vol.2 (1954)).

  5. S. M. Nikol'skii, “Approximation of periodic functions by trigonometric polynomials,” Trudy Matem. Inst. im. Steklova, Akad. Nauk SSSR,15 (1945).

  6. N. P. Korneichuk, “Asymptotic estimates of remainders for the approximation of periodic functions satisfying a Lipschitz condition by Bernshtein interpolation sums,” Nauchn. Dokl. Vys, Shkoi., No. 1 (1959).

  7. N. P. Korneichuk, “Approximation of functions of a Lipschitz class by means of linear methods,” Dokl. Akad. Nauk URSR, No. 7 (1961).

  8. G. P. Gubanov, “Asymptotic estimates of the remainder for the approximation of functions of two variables by Bernshtein-Rogozinski sums,” Nauchn. Zapisk. Dnepropetrovskii Univ.,77 (1962).

  9. S. B. Stechkin, “Approximation of continuous periodic functions by Favar sums,” Trudy Matem. Inst. im Steklova, Akad. Nauk SSSR,109 (1971).

  10. Wang Xing-Hua, “The exact constant of approximation of a continuous function by the Jackson singular integral,” Acta Matem. Sinica,14, No.2 (1964).

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, USSR

    V. T. Gavrilyuk

Authors
  1. V. T. Gavrilyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol.25, No. 5, pp. 637–648, September–October, 1973.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gavrilyuk, V.T. Approximation of continuous periodic functions of one or two variables by Rogozinski polynomials of interpolation type. Ukr Math J 25, 530–537 (1973). https://doi.org/10.1007/BF01091946

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01091946

Keywords

Search

Navigation