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Ukrainian Mathematical Journal

, Volume 56, Issue 11, pp 1738–1747 | Cite as

Best Polynomial Approximations in L2 and Widths of Some Classes of Functions

  • S. B. Vakarchuk
  • A. N. Shchitov
Article

Abstract

We obtain the exact values of extremal characteristics of a special form that connect the best polynomial approximations of functions f(x) ∈ L 2 r (r ∈ ℤ+) and expressions containing moduli of continuity of the kth order ωk(f(r), t). Using these exact values, we generalize the Taikov result for inequalities that connect the best polynomial approximations and moduli of continuity of functions from L2. For the classes \(\mathcal{F}\) (k, r, Ψ*) defined by ω k(f(r), t) and the majorant \(\Psi _ (t) = t^{4k/\pi ^2 }\), we determine the exact values of different widths in the space L2.

Keywords

Special Form Polynomial Approximation Extremal Characteristic Good Polynomial Approximation 
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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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • S. B. Vakarchuk
    • 1
  • A. N. Shchitov
    • 1
  1. 1.Ukrainian Academy of Customs ServiceDnepropetrovskUkraine

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