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Ukrainian Mathematical Journal

, Volume 53, Issue 12, pp 1998–2013 | Cite as

Approximation of \(\overline \psi\)-Integrals of Periodic Functions by de la Vallée-Poussin Sums (Low Smoothness)

  • V. I. Rukasov
  • S. O. Chaichenko
Article
  • 21 Downloads

Abstract

We investigate the asymptotic behavior of the upper bounds of deviations of linear means of Fourier series from the classes \(C_\infty ^{\psi}\). In particular, we obtain asymptotic equalities that give a solution of the Kolmogorov–Nikol'skii problem for the de la Vallée-Poussin sums on the classes \(C_\infty ^{\overline \psi }\).

Keywords

Asymptotic Behavior Fourier Series Periodic Function Asymptotic Equality Skii Problem 
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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • V. I. Rukasov
    • 1
  • S. O. Chaichenko
    • 1
  1. 1.Slavyansk Pedagogic InstituteSlavyansk

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