Skip to main content
Log in

Best piecewise-monotone approximation and the Banach indicatrix

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

Literature cited

  1. G. H. Hardy, D. E. Littlewood, and G. Pólya, Inequalities, Cambridge Univ. Press, Cambridge (1964).

    Google Scholar 

  2. A. A. Sevast'yanov, “Piecewise-monotone approximation and Φ-variations,” Anal. Math.,1, No. 2, 141–164 (1975).

    Google Scholar 

  3. S. Banach, “Sur les lignes rectifiables et les surfaces dont l'aire est finie,” Fund. Math.,7, 225–236 (1925).

    Google Scholar 

  4. E. A. Sevast'yanov, “Influence of the rate of rational and piecewise-monotone approximations on the structural properties of functions,” Candidate's Dissertation, Moscow (1974).

  5. K. I. Oskolkov, “Generalized variation, the Banach indicatrix, and uniform convergence of Fourier series,” Mat. Zametki,12, No. 3, 313–324 (1972).

    Google Scholar 

  6. Z. A. Chanturiya, “The modulus of variation of a function and its application in the theory of Fourier series,” Dokl. Akad. Nauk SSSR,214, No. 1, 63–66 (1974).

    Google Scholar 

  7. P. Petrushev and V. Kh. Khristov, “Convergence of Fourier series in the Hausdorff metric,” Pliska,1, 21–36 (1977).

    Google Scholar 

  8. K. I. Oskolkov, “On Fourier sums for the Banach indicatrix,” Mat. Zametki,15, No. 4, 527–532 (1974).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki, Vol. 26, No. 1, pp. 77–87, July, 1979.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sevast'yanov, E.A. Best piecewise-monotone approximation and the Banach indicatrix. Mathematical Notes of the Academy of Sciences of the USSR 26, 528–535 (1979). https://doi.org/10.1007/BF01140276

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01140276

Navigation