Skip to main content
SpringerLink
Log in

On the best quadrature formulas for some classes of continuous functions

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

Abstract

We obtain the best quadrature formulas for classes of continuous functions defined by various restrictions on the moduli of continuity with respect to increase and decrease.

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

References

  1. I. R. Nezhmetdinov, “One-sided moduli of continuity and exact estimates of harmonic functions,” in: Proceedings of a Seminar on Boundary-Value Problems [in Russian], Kazan University, Kazan (1984), pp. 18–23.

    Google Scholar 

  2. I. R. Nezhmetdinov, “One-sided moduli of continuity and exact estimates of harmonic functions,” in: Proceedings of a Seminar on Boundary-Value Problems [in Russian], Kazan University, Kazan (1985), pp. 26–31.

    Google Scholar 

  3. N. P. Komeichuk, Extremal Problems in the Theory of Approximation [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  4. S. M. Nikol’skii, Quadrature Formulas [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  5. G. K. Lebed’, “On quadrature formulas with the least estimate of a residual on some classes of functions,” Mat. Tametki, 3, No. 5, 577–596 (1968).

    MathSciNet  Google Scholar 

  6. N. P. Korneichuk, “Best cubature formulas for some classes of functions of many variables,” Mat. Zametki, 3, No. 5, 565–576.

  7. V. P. Motornyi, “On a best cubature formula of the form \(\sum\nolimits_{i = 1}^n {p_i f(x_i )} \) for some classes of periodic differentiable functions,” Izv. Akad. Nauk SSSR, Ser. Mat., 38, No. 3, 583–614 (1974).

    MathSciNet  Google Scholar 

  8. V. F. Babenko and O. V. Polyakov, “Exact estimates of some characteristics of classes of periodic functions,” in: Theory of Approximation and Related Problems of Analysis and Topology [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1987), pp. 9–14.

    Google Scholar 

  9. V. F. Babenko and O. V. Polyakov, “Approximation in mean for some classes of continuous functions,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 2, 13–21 (1995).

Download references

Author information

Authors and Affiliations

  1. Dnepropetrovsk University, Dnepropetrovsk

    O. V. Polyakov

Authors
  1. O. V. Polyakov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 9, pp. 1284–1288, September, 1998.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Polyakov, O.V. On the best quadrature formulas for some classes of continuous functions. Ukr Math J 50, 1468–1472 (1998). https://doi.org/10.1007/BF02525255

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02525255

Keywords

Search

Navigation