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Asymptotics of the values of approximations in the mean for classes of differentiable functions by using biharmonic Poisson integrals

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Abstract

We obtain complete asymptotic expansions for the exact upper bounds of the approximations of functions from the classes W r1 , r ∈ N, and \(\overline W _1^r \), r ∈ N\{1}, by their biharmonic Poisson integrals.

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Authors and Affiliations

  1. Volyn University, Luts’k

    Yu. I. Kharkevych & I. V. Kal’chuk

Authors
  1. Yu. I. Kharkevych
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  2. I. V. Kal’chuk
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 8, pp. 1105–1115, August, 2007.

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Kharkevych, Y.I., Kal’chuk, I.V. Asymptotics of the values of approximations in the mean for classes of differentiable functions by using biharmonic Poisson integrals. Ukr Math J 59, 1224–1237 (2007). https://doi.org/10.1007/s11253-007-0082-4

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  • DOI: https://doi.org/10.1007/s11253-007-0082-4

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