Estimates for the Approximations of the Classes of Analytic Functions by Interpolation Analogs of the De-La-Vallée–Poussin Sums
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 β,s ψ 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 β ψ H ω generated by convex moduli of continuity ω(t). Under the conditions n − p → ∞ and p → ∞, the indicated estimates turn into asymptotic equalities.
English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 1, pp 50-65.
Citation Example: Voitovych V. A. Estimates for the Approximations of the Classes of Analytic Functions by Interpolation Analogs of the De-La-Vallée–Poussin Sums // Ukr. Mat. Zh. - 2014. - 66, № 1. - pp. 49–62.