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Some sharp inequalities between best approximations and moduli of continuity

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Literature Cited

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

    Google Scholar 

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

    Google Scholar 

  3. N. P. Korneichuk, “Best uniform approximation of differentiable functions,” Dokl. Akad. Nauk SSSR,141, No. 2, 304–307 (1961).

    Google Scholar 

  4. J. Favard, “Best methods of approximation of certain classes of functions by trigonometric polynomials,” Bull. Sci. Math.,61, 209–224, 243–256 (1937).

    Google Scholar 

  5. N. I. Akhiezer and M. G. Krein, “Best approximation by trigonometric sums of differentiable periodic functions,” Dokl. Akad. Nauk SSSR,15, No. 3, 107–112 (1937).

    Google Scholar 

  6. N. I. Akhiezer, Lectures on Approximation Theory [in Russian], Nauka, Moscow (1965).

    Google Scholar 

  7. G. H. Hardy, D. E. Littlewood, and G. Polya, Inequalities [Russian translation] IL, Moscow (1948).

    Google Scholar 

  8. G. E. Shilov, “Inequalities among derivatives,” Sb. Nauchn. Stud. Rabot Un-ta, Moscow, 17–27 (1937).

  9. A. N. Kolmogorov, “Inequalities among upper bounds of sequences of derivatives of an arbitrary function on an infinite interval,” Uch. Zap. MGU,30, 3–16 (1939).

    Google Scholar 

  10. S. M. Nikol'skii, “Mean approximation of functions by trigonometric polynomials,” Izv. Akad. Nauka SSSR, Ser. Matem.,10, No. 2, 207–256 (1946).

    Google Scholar 

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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 12, No. 6, pp. 1283–1291, November–December, 1971.

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Zhuk, V.V. Some sharp inequalities between best approximations and moduli of continuity. Sib Math J 12, 924–930 (1971). https://doi.org/10.1007/BF00966535

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  • DOI: https://doi.org/10.1007/BF00966535

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