Skip to main content
SpringerLink
Log in

The rational approximation of convex functions of the class Lip α

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

Abstract

It is proved that if a function f(x) is convex on [a, b] and f ∈ LipK(f)α, 0<α<1, then the least uniform deviation of this function from rational functions of degree not higher than n does not exceed

(v is a natural number; C(α, v) depends only onα andv; K(f) is a Lipschitz constant; and

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

Literature cited

  1. P. Szüsz and P. Turan, “On the constructive theory of functions, I,” Magyar Tud. Acad. Mat. Kutató Intér. Közl., A9, No. 3, 495–502 (1965).

    Google Scholar 

  2. G. Freud, “Uber die Approximation reeller Funktionen durch rationale gebrochene Funktionen,” Acta Math. Acad. Sci. Hung.,17, 313–324 (1966).

    Google Scholar 

  3. V. A. Popov, “On the rational approximation of functions of the class Vr,” Acta Math. Acad. Sci. Hung., 25,(1–2), 61–65 (1974).

    Google Scholar 

  4. A. A. Abdugapparov, ldOn rational approximations of convex functions,” Izv. Akad. Nauk UzSSR, Ser. Fiz.-Matem., No. 2, 3–9 (1969).

    Google Scholar 

  5. A. P. Bulanov, “Rational approximations of convex functions with a given modulus of continuity,” Matem. Sb.,84, No. 3, 476–494 (1971).

    Google Scholar 

  6. A. A. Abdugapparov, “On rational approximations of convex functions of the class Lipα,” Izv. Akad. Nauk UzSSR, Ser. Fiz.-Matem., No. 6, 5–10 (1972).

    Google Scholar 

  7. G. Freud, “On rational approximation of absolutely continuous functions,” Studia Sci. Math. Hung.,3, 383–386 (1968).

    Google Scholar 

  8. V. A. Popov and J. Szabados, “On a general localization theorem and some applications in the theory of rational approximation,” Acta Math. Acad. Sci. Hung.,25(1–2), 165–170 (1974).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    A. Khatamov

Authors
  1. A. Khatamov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 18, No. 6, pp. 845–854, December, 1975.

In conclusion, the author thanks E. P. Dolzhenko for stating the problem and guiding my work.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khatamov, A. The rational approximation of convex functions of the class Lip α. Mathematical Notes of the Academy of Sciences of the USSR 18, 1092–1096 (1975). https://doi.org/10.1007/BF01099987

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01099987

Keywords

Search

Navigation