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Approximation of the Classes \(C^{{\bar \psi }} H_{\omega }\) by de la Vallée-Poussin Sums

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Abstract

We investigate the problem of the approximation of the classes \(C^{{\bar \psi }} H_{\omega }\) introduced by Stepanets in 1996 by the de la Valée-Poussin sums. We obtain asymptotic equalities that give a solution of the Kolmogorov–Nikol'skii problem for the de la Valée-Poussin sums on the classes \(C^{{\bar \psi }} H_{\omega }\) in several important cases.

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REFERENCES

  1. A. I. Stepanets, Approximation of \(\overline \psi \) -Integrals of Periodic Functions by Fourier Sums [in Russian], Preprint No. 96.11, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1996).

    Google Scholar 

  2. A. I. Stepanets, “Several statements for convex functions,” Ukr. Mat. Zh., 51, No. 5, 688–702 (1999).

    Google Scholar 

  3. A. I. Stepanets, “Rate of convergence of a group of deviations on sets of \(\overline \psi \)-integrals,” Ukr. Mat. Zh., 51, No. 12, 1673–1693 (1999).

    Google Scholar 

  4. A. V. Efimov, “On the approximation of periodic functions by de la Vallée-Poussin sums. II,” Izv. Akad. Nauk SSSR, Ser. Mat., 24, 431–468 (1960).

    Google Scholar 

  5. A. F. Timan, “Approximation properties of linear summation methods for Fourier series,” Izv. Akad. Nauk SSSR, Ser. Mat., 17, 99–134 (1953).

    Google Scholar 

  6. V. I. Rukasov and S. O. Chaichenko, “Approximation of \(\overline \psi \)-integrals of 2π?-periodic functions by de la Vallée-Poussin sums,” in: Fourier Series: Theory and Applications [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1998), pp. 242–254.

    Google Scholar 

  7. A. I. Stepanets, Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987).

    Google Scholar 

  8. A. I. Stepanets, “Approximation in spaces of locally integrable functions,” Ukr. Mat. Zh., 46, No. 5, 597–625 (1994).

    Google Scholar 

  9. A. I. Stepanets, “Classification and approximation of periodic functions and rate of convergence of their Fourier series,” Izv. Akad. Nauk SSSR, Ser. Mat., 50, No. 1, 101–136 (1986).

    Google Scholar 

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Authors and Affiliations

  1. Slavyansk Pedagogic Institute, Slavyansk

    V. I. Rukasov & S. O. Chaichenko

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  1. V. I. Rukasov
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  2. S. O. Chaichenko
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Rukasov, V.I., Chaichenko, S.O. Approximation of the Classes \(C^{{\bar \psi }} H_{\omega }\) by de la Vallée-Poussin Sums. Ukrainian Mathematical Journal 54, 839–851 (2002). https://doi.org/10.1023/A:1021643732395

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