Skip to main content
Log in

On the Best Linear Approximation Method for Hölder Classes

  • Published:
Ukrainian Mathematical Journal Aims and scope

We find the exact values of one-dimensional linear widths for the Hölder classes of functions in the space C and the value of the best approximation of the Hölder classes of functions by a wide class of linear positive methods.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Yu. I. Grigoryan, “Widths of some sets in functional spaces,” Mat. Zametki, 13, No. 5, 637–646 (1973).

    MathSciNet  Google Scholar 

  2. P. R. Halmos, Measure Theory, D. Van Nostrand, New York (1950).

    Book  MATH  Google Scholar 

  3. M. A. Krasnosel’skii, E. A. Lifshits, and A.V. Sobolev, Positive Linear Systems: Method of Positive Operators [in Russian], Nauka, Moscow (1985).

    MATH  Google Scholar 

  4. N. P. Korneichuk, “Exact value of the best approximations and widths of some classes of functions,” Dokl. Akad. Nauk SSSR, 150, No. 6, 1218–1220 (1963).

    MathSciNet  Google Scholar 

  5. N. P. Korneichuk, “Extremal values of functionals and the best approximation on classes of periodic functions,” Izv. Akad. Nauk SSSR, Ser. Mat., 5, No. 1, 93–124 (1971).

    MathSciNet  Google Scholar 

  6. N. P. Korneichuk, “On the methods of investigation of extremal problems of the theory of best approximation,” Usp. Mat. Nauk, 29, No. 3, 9–42 (1974).

    Google Scholar 

  7. N. P. Korneichuk, Extremal Problems of Approximation Theory [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  8. N. P. Korneichuk, Splines in Approximation Theory [in Russian], Nauka, Moscow (1984).

    Google Scholar 

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

    Google Scholar 

  10. N. P. Korneichuk, “On linear widths of H ω classes,” Ukr. Mat. Zh., 48, No. 9, 1255–1264 (1996); English translation: Ukr. Math. J., 48, No. 9, 1423–1433 (1996).

  11. 11. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series: Special Functions. Additional Chapters [in Russian], Fizmatlit, Moscow (2003).

    MATH  Google Scholar 

  12. V. I. Ruban, “Even widths of the classes W (r) H ω in the space C 2π ,Mat. Zametki, 15, No. 3, 387–392 (1974).

    MathSciNet  Google Scholar 

  13. V. M. Tikhomirov, “Widths of sets in functional spaces and the theory of best approximations,” Usp. Mat. Nauk, 15, No. 3, 81–120 (1960).

    Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 9, pp. 1265–1284, September, 2015.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Skorokhodov, D.S. On the Best Linear Approximation Method for Hölder Classes. Ukr Math J 67, 1425–1446 (2016). https://doi.org/10.1007/s11253-016-1163-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-016-1163-z

Keywords

Navigation