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Sharpness of Jackson's inequality for individual functions

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Abstract

The asymptotic behavior of the ratioE n(f)/Ω (f), π/n) is studied for individual functions f∃C in the sense of upper and lower limits.

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Literature cited

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

    Google Scholar 

  2. S. M. Nikol'skik, “Interpolation and best approximation of differentiable periodic functions by trigonometric polynomials,” Izv. Akad. Nauk SSSR, Ser. Mat.,10, No. 5, 393–410 (1946).

    Google Scholar 

  3. V. N. Temlyakov, “Asymptotic behavior of best approximations of continuous functions,” Izv. Akad. Nauk SSSR, Ser. Mat.,41, No. 3, 587–606 (1977).

    Google Scholar 

  4. V. N. Temlyakov, “Asymptotic behavior of best approximations of continuous functions,” Mat. Sb.,110, (152), No. 3, 399–413 (1979).

    Google Scholar 

  5. G. Ya. Doronin, “Inequalities for approximations by trigonometric polynomials,” Dokl. Akad. Nauk SSSR,69, No. 4, 487–490 (1949).

    Google Scholar 

  6. K. I. Oskolkov, “Estimate of approximation of continuous functions by sequences of Fourier sums,” Tr. Mat. Inst. Akad. Nauk SSSR,134, 240–253 (1975).

    Google Scholar 

  7. N. P. Korneichuk, “Sharp constant in Jackson's theorem on best uniform approximation of continuous periodic functions,“ Dokl. Akad. Nauk SSSR,145, No. 3, 514–515 (1962).

    Google Scholar 

  8. S. N. Bernshtein, “Best approximation of ¦xc¦p,” Dokl. Akad. Nauk SSSR,18, 379–384 (1938).

    Google Scholar 

  9. S. M. Nikol'skii, “Best approximation of functions whose s-th derivative has discontinuities of the first kind,” Dokl. Akad. Nauk SSSR,55, No. 2, 99–102 (1947).

    Google Scholar 

  10. V. V. Zhuk, “Sharp inequalities between uniform approximations of periodic functions,” Dokl. Akad. Nauk SSSR,201, No. 2, 263–265 (1971).

    Google Scholar 

  11. A. A. Ligun, “Sharp constants of approximation of differentiable period functions,” Mat. Zametki,14, No. 1, 21–30 (1973).

    Google Scholar 

  12. O. V. Davydov, “Sharp constant in a Jackson type inequality for spline-approximation,” in: Questions of Analysis and Approximation [in Russian], Inst. Mat., Academy of Sciences of the Ukrainian SSR, Kiev (1989), pp. 38–51.

    Google Scholar 

  13. O. V. Davydov, “Asymptotic behavior of best uniform approximations of individual functions by splines,” Ukr. Mat. Zh.,42, No. 1, 59–64 (1990)

    Google Scholar 

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Authors and Affiliations

  1. Dnepropetrovsk University, USSR

    O. V. Davydov

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  1. O. V. Davydov
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 11, pp. 1469–1475, November, 1990.

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Davydov, O.V. Sharpness of Jackson's inequality for individual functions. Ukr Math J 42, 1311–1316 (1990). https://doi.org/10.1007/BF01066185

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  • DOI: https://doi.org/10.1007/BF01066185

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