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Ukrainian Mathematical Journal

, Volume 70, Issue 9, pp 1331–1344 | Cite as

Jackson–Stechkin-Type Inequalities for the Approximation of Elements of Hilbert Spaces

  • V. F. Babenko
  • S. V. Konareva
Article
  • 45 Downloads

We introduce new characteristics for elements of Hilbert spaces, namely, their generalized moduli of continuity ωφ(x, Lp,V ([0, δ])) and obtain new exact Jackson–Stechkin-type inequalities with these moduli of continuity for the approximation of elements of Hilbert spaces. These results include numerous well-known inequalities for the approximation of periodic functions by trigonometric polynomials, approximation of nonperiodic functions by entire functions of exponential type, similar results for almost periodic functions, etc. Some of these results are new even in these classical cases.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • V. F. Babenko
    • 1
  • S. V. Konareva
    • 1
  1. 1.Dnepr National UniversityDneprUkraine

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