Estimates for the Approximations of the Classes of Analytic Functions by Interpolation Analogs of the De-La-Vallée–Poussin Sums

  • V. A. Voitovych

Abstract

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 ∈, 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.
Published
25.01.2014
How to Cite
Voitovych, V. A. “Estimates for the Approximations of the Classes of Analytic Functions by Interpolation Analogs of the De-La-Vallée–Poussin Sums”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, no. 1, Jan. 2014, pp. 49–62, http://umj.imath.kiev.ua/index.php/umj/article/view/2110.
Section
Research articles