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Ukrainian Mathematical Journal

, Volume 51, Issue 5, pp 764–780 | Cite as

Several statements for convex functions

  • A. I. Stepanets
Article

Abstract

For the setM of convex-downward functions Ψ (•) vanishing at infinity, we present its decomposition into subsets with respect to the behavior of special characteristics η (Ψ;•) and μ(Ψ;•) of these functions. We study geometric and analytic properties of the elements of the subsets obtained, which are necessary for the investigation of problems of the theory of approximation for classes of convolutions.

Keywords

Fourier Series Convex Function Analytic Property Trigonometric Polynomial Approximation Characteristic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    A. I. Stepanets, “The convergence rate of Fourier series on the classes of\(\bar \psi \),”Ukr. Mat. Zh.,49, No. 8, 1069–1113 (1997).zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    A. I. Stepanets,Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987).zbMATHGoogle Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

  • A. I. Stepanets

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