Skip to main content
SpringerLink
Log in

Approximation of functions from the class \({\ifmmode\expandafter\hat\else\expandafter\^\fi{C}}^\psi_{\beta,\infty}\) by Poisson biharmonic operators in the uniform metric

  • Published:
Ukrainian Mathematical Journal Aims and scope

We obtain asymptotic equalities for upper bounds of approximations of functions from the class \({\ifmmode\expandafter\hat\else\expandafter\^\fi{C}}^\psi_{\beta,\infty}\) by Poisson biharmonic operators in the uniform metric.

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. A. I. Stepanets, “Classes of functions defined on the real axis and their approximation by entire functions. I,” Ukr. Mat. Zh., 42, No. 1, 102–112 (1990).

    Article  MathSciNet  Google Scholar 

  2. A. I. Stepanets, “Classes of functions defined on the real axis and their approximation by entire functions. II,” Ukr. Mat. Zh., 42, No. 2, 210–222 (1990).

    Article  MathSciNet  Google Scholar 

  3. A. I. Stepanets, Methods of Approximation Theory [in Russian], Vol. 2, Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev (2002).

    Google Scholar 

  4. A. I. Stepanets, Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987).

    MATH  Google Scholar 

  5. A. I. Stepanets, Methods of Approximation Theory [in Russian], Vol. 1, Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev (2002).

    Google Scholar 

  6. S. Kaniev, “On the deviation of functions biharmonic in a disk from their boundary values,” Dokl. Akad. Nauk SSSR, 153, No. 5, 995–998 (1963).

    MathSciNet  Google Scholar 

  7. M. G. Dzimistarishvili, “Approximation of classes of continuous functions by Zygmund operators,” in: Approximation by Zygmund Operators and Best Approximation [in Russian], Preprint No. 89.25, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1989), pp. 3–42.

    Google Scholar 

  8. M. G. Dzimistarishvili, “Approximation of the classes \({\ifmmode\expandafter\hat\else\expandafter\^\fi{L}}^\psi_{\beta,1}\) in the metric of L 1,” in: Harmonic Analysis and Development of Approximation Methods [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1989), pp. 52–54.

    Google Scholar 

  9. M. G. Dzimistarishvili, On the Behavior of Upper Bounds of Deviations of Steklov Operators [in Russian], Preprint No. 90.25, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1989), pp. 3–29.

    Google Scholar 

  10. V. I. Rukasov, “Approximation of functions defined on the real axis by de la Vallée-Poussin operators,” Ukr. Mat. Zh., 44, No. 5, 682–691 (1992).

    Article  MathSciNet  Google Scholar 

  11. V. I. Rukasov and S. O. Chaichenko, “Approximation of the Poisson integrals of functions defined on the real axis by de la Vallée-Poussin operators,” in: Problems in Approximation Theory of Functions and Related Questions [in Ukrainian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv (2005), pp. 228–237.

    Google Scholar 

  12. O. V. Ostrovs’ka, “Approximation of classes of continuous functions by Zygmund operators,” in: Approximation of Classes of Continuous Functions Defined on the Real Axis [in Ukrainian], Preprint No. 94.5, Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv (1994), pp. 1–15.

    Google Scholar 

  13. L. A. Repeta, “Approximation of functions of the classes \({\ifmmode\expandafter\hat\else\expandafter\^\fi{C}}^\psi_{\beta,\infty}\) by operators of the form \(U^{\varphi,F}_{\sigma}\),” in: Fourier Series: Theory and Applications [in Russian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev (1992), pp. 147–154.

    Google Scholar 

  14. I. I. Stepanets’ and I. V. Sokolenko, “Approximation of the \({\ifmmode\expandafter\bar\else\expandafter\=\fi{\psi }}\)-integrals of functions defined on the real axis by Fourier operators,” Ukr. Mat. Zh., 56, No. 7, 960–965 (2004).

    MathSciNet  Google Scholar 

  15. I. V. Kal’chuk, “Approximation of (ψ, β)-differentiable functions defined on the real axis by Weierstrass operators,” Ukr. Mat. Zh., 59, No. 9, 1201–1220 (2007).

    MATH  MathSciNet  Google Scholar 

  16. Yu. I. Kharkevych and T. V. Zhyhallo, “Approximation of functions defined on the real axis by Poisson biharmonic operators,” in: Problems in Approximation Theory of Functions and Related Questions” [in Ukrainian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv (2005), pp. 295–310.

    Google Scholar 

  17. L. I. Bausov, “Linear methods of summation of Fourier series with given rectangular matrices. I,” Izv. Vyssh. Uchebn. Zaved., 46, No. 3, 15–31 (1965).

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Volyn’ National University, Luts’k, Ukraine

    Yu. I. Kharkevych & T. V. Zhyhallo

Authors
  1. Yu. I. Kharkevych
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. V. Zhyhallo
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 5, pp. 669–693, May, 2008.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kharkevych, Y.I., Zhyhallo, T.V. Approximation of functions from the class \({\ifmmode\expandafter\hat\else\expandafter\^\fi{C}}^\psi_{\beta,\infty}\) by Poisson biharmonic operators in the uniform metric. Ukr Math J 60, 769–798 (2008). https://doi.org/10.1007/s11253-008-0093-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-008-0093-9

Keywords

Search

Navigation