Skip to main content
SpringerLink
Log in

Uniform approximation of functions on an interval

  • 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

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

Literature cited

  1. S. M. Nikol'skii, “On the best polynomial approximation of functions satisfying a Lipschitz condition,” Izv. Akad. Nauk SSSR, Ser. Mat.,10, No. 3, 295–317 (1946).

    Google Scholar 

  2. A. F. Timan, The Approximation Theory of Functions of a Real Variable [in Russian], Fizmatgiz, Moscow (1960).

    Google Scholar 

  3. V. K. Izyadyk, Introduction into the Theory of Uniform Approximation of Functions [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  4. Yu. A. Brudnyi, “A generalization of a theorem of A. F. Timan,” Dokl. Akad. Nauk SSSR,188, No. 6, 1237–1240 (1963).

    Google Scholar 

  5. S. B. Stechkin, “On the order of best approximations of continuous functions,” Izv. Akad. Nauk SSSR, Ser. Mat.,15, No. 3, 219–242 (1951).

    Google Scholar 

  6. N. K. Bari and S. B. Stechkin, “Best approximations and differential properties of two conjugate functions,” Tr. Mosk. Mat. Obshch.,5, 483–522 (1956).

    Google Scholar 

  7. S. K. Lozinskii, “The converse of Jackson's theorem,” Dokl. Akad. Nauk SSSR,83, No. 5, 645–647 (1952).

    Google Scholar 

  8. M. Hasson. “The sharpness of Timan's theorem on differentiable functions,” J. Approx. Theory,35, No. 3, 264–274 (1982).

    Google Scholar 

  9. I. A. Shevchuk, “On k-th moduli of continuity of functions of a real or a complex variable,” Konstruktivnaya Teoriya Funktsii,77, 191–194 (1980) Sofiya.

    Google Scholar 

  10. I. I. Ibragimov, “On the asymptotic value of the best approximation of functions with a real singular point,” Izv. Akad. Nauk SSSR, Ser. Mat.,10, No. 5, 429–456(1946).

    Google Scholar 

  11. R. M. Trigub, “Approximation of functions by polynomials with integral coefficients,” Izv. Akad. Nauk SSSR, Ser. Mat.,26, No. 2, 261–280 (1962).

    Google Scholar 

  12. H. Whitney, “On functions with bounded n-th differences,” J. Math. Pures Appl.,36, No.1, 67–95 (1957).

    Google Scholar 

  13. S. A. Telyakovskii, “Two theorems on the approximation of functions by algebraic polynomials,” Mat. Sb.,70, No. 2, 252–265 (1966).

    Google Scholar 

  14. I. A. Shevchuk, “Some remarks on functions of the type of a modulus of continuity of order k ≥ 2,” In: Problems of the Approximation Theory of Functions and Its Applications [in Russian], Izd. Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1976), pp. 194–199.

    Google Scholar 

  15. T. F. Xie, “On two problems of Haason,” Approx. Theory Appl.,1, No. 2, 137–144 (1985).

    Google Scholar 

  16. E. P. Dolzhenko and E. A. Sevast'yanov, “On the dependence of The properties of functions on the rate of their approximation by polynomials,” Izv. Akad. Nauk SSSR, Ser. Mat.,42, No. 2, 270–304 (1978).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, USSR

    I. A. Shevehuk

Authors
  1. I. A. Shevehuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 40, No. 1, pp. 36–48, July, 1986.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shevehuk, I.A. Uniform approximation of functions on an interval. Mathematical Notes of the Academy of Sciences of the USSR 40, 521–528 (1986). https://doi.org/10.1007/BF01159566

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01159566

Keywords

Search

Navigation