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Exact order of relative widths of classes W r1 in the space L 1

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Abstract

We determine the exact order of relative widths of classes W r1 of periodic functions in the space L 1 as n → ∞ under restrictions on higher derivatives of approximating functions.

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References

  1. A. N. Kolmogorov, “On the best approximation of functions of a given functional class,” in: Mathematics and Mechanics, Selected Works [in Russian], Nauka, Moscow (1985), pp. 186–189.

    Google Scholar 

  2. V. N. Konovalov, “Estimation of Kolmogorov-type widths for classes of differentiable periodic functions,” Mat. Zametki, 35, No. 3, 369–380 (1984).

    MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  4. V. F. Babenko, “Approximation in the mean under restrictions on the derivatives of approximating functions,” in: Problems of Analysis and Approximations [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1989), pp. 9–18.

    Google Scholar 

  5. V. F. Babenko, “On the best uniform approximations by splines under restrictions on their derivatives,” Mat. Zametki, 50, No. 6, 24–30 (1991).

    MATH  MathSciNet  Google Scholar 

  6. V. F. Babenko, “On the best L 1-approximations by splines under restrictions on their derivatives,” Mat. Zametki, 51, No. 5, 12–19 (1992).

    MATH  MathSciNet  Google Scholar 

  7. V. F. Babenko, L. Azar, and N. V. Parfinovich, “On the approximation of classes of periodic functions by splines under restrictions on their derivatives,” in: Fourier Series: Theory and Applications [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv (1998), pp. 18–29.

    Google Scholar 

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

    Google Scholar 

  9. V. F. Babenko, “On the relative widths of classes of functions with bounded mixed derivative,” East J. Approxim., 2, No. 3, 319–330 (1996).

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Dnipropetrovs’k University, Dnipropetrovs’k

    N. V. Parfinovych

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  1. N. V. Parfinovych
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 10, pp. 1409–1417, October, 2005.

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Parfinovych, N.V. Exact order of relative widths of classes W r1 in the space L 1 . Ukr Math J 57, 1652–1662 (2005). https://doi.org/10.1007/s11253-006-0019-3

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  • DOI: https://doi.org/10.1007/s11253-006-0019-3

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