We establish two-sided estimates for the exact upper bounds of approximations by the interpolation analogs of the de-la-Vallée-Poussin sums on the classes of 2π -periodic functions C ψ β,s specified by the sequences ψ(k) and shifts of the argument β , β ∈ ℝ, under the condition that the sequences ψ(k) satisfy the d’Alembert D q , q ∈ (0, 1), condition. Similar estimates are obtained for the classes C ψ β H ω generated by convex moduli of continuity ω(t). Under the conditions n − p → ∞ and p → ∞, the indicated estimates turn into asymptotic equalities.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 1, pp. 49–62, January, 2014.
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Voitovych, V.A. Estimates for the Approximations of the Classes of Analytic Functions by Interpolation Analogs of the De-La-Vallée–Poussin Sums. Ukr Math J 66, 50–65 (2014). https://doi.org/10.1007/s11253-014-0911-1
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DOI: https://doi.org/10.1007/s11253-014-0911-1