Ukrainian Mathematical Journal

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

Several statements for convex functions

  • A. I. Stepanets


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.


Fourier Series Convex Function Analytic Property Trigonometric Polynomial Approximation Characteristic 
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  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

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  • A. I. Stepanets

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