Skip to main content
SpringerLink
Log in

Lower bounds for the deviations of the best linear methods of approximation of continuous functions by trigonometric polynomials

  • Published:
Ukrainian Mathematical Journal Aims and scope

In the case of uniform approximation of continuous periodic functions of one variable by trigonometric polynomials, we obtain lower bounds for the Jackson constants of the best linear methods of approximation.

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

Similar content being viewed by others

References

  1. N. P. Korneichuk, Exact Constants in Approximation Theory [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  2. N. P. Korneichuk, “Exact constant in the Jackson theorem on the best uniform approximation of continuous periodic functions,” Dokl. Akad. Nauk SSSR, 145, No. 3, 514–515 (1962).

    MathSciNet  Google Scholar 

  3. N. P. Korneichuk, “On the exact constant in the Jackson inequality for continuous periodic functions,” Mat. Zametki, 32, No. 5, 669–674 (1982).

    MathSciNet  Google Scholar 

  4. V. V. Shalaev, Some Exact Estimates for Approximation of Functions by Linear Polynomial Methods [in Russian], Candidate-Degree Thesis (Physics and Mathematics), Dnepropetrovsk (1980).

  5. S. B. Stechkin, “Approximation of continuous periodic functions by Favard sums,” Tr. Mat. Inst. Akad. Nauk SSSR, 119, 26–34 (1971).

    Google Scholar 

  6. N. P. Korneichuk, “On estimation of approximation of functions of the class H α by trigonometric polynomials,” in: Investigations in Contemporary Problems of the Constructive Theory of Functions [in Russian], 1 (1961), pp. 148–154.

  7. V. M. Tikhomirov, Some Problems of Approximation Theory [in Russian], Moscow University, Moscow (1976).

    Google Scholar 

  8. S. M. Nikol’skii, “Approximation of functions by trigonometric polynomials in the mean,” Izv. Akad. Nauk SSSR, Ser. Mat., 207–256 (1946).

  9. V. V. Shalaev, On the Error of the Best Linear Polynomial Method on the Class H ω of Periodic Functions [in Russian], Dep. Ukr. NIIITI, Dnepropetrovsk (1980).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dnepropetrovsk National University of Railway Transport, Dnepropetrovsk, Ukraine

    S. A. Pichugov

Authors
  1. S. A. Pichugov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 5, pp. 662–673, May, 2012.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pichugov, S.A. Lower bounds for the deviations of the best linear methods of approximation of continuous functions by trigonometric polynomials. Ukr Math J 64, 752–766 (2012). https://doi.org/10.1007/s11253-012-0676-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-012-0676-3

Keywords

Search

Navigation