A. Serdyuk

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20112025

most citedApproximation of classes of analytic functions by de la Vallee Poussin sums in uniform metric

7 citations · 16 across the 24 of their papers we have counts for

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4 papers · 1 filter

math.CA2023

Estimates of approximations by interpolation trigonometric polynomials on the classes of convolutions of high smoothness

A. S. Serdyuk, T. A. Stepaniuk

We establish interpolation analogues of Lebesgue type inequalities on the sets of $C_{β}^{ψ} L_{1}$ $2 π$ -periodic functions $f$ , which are representable as convolutions of generating ke…

math.CA2023

Asymptotic estimates for the widths of classes of functions of high smoothness

A. S. Serdyuk, I. V. Sokolenko

We find two-sided estimates for Kolmogorov, Bernstein, linear and projection widths of the classes of convolutions of $2 π$ -periodic functions $φ$ , such that $∥ φ ∥_{2} \leq 1$ , with fix…

math.CA2023

Approximation of generalized Poisson integrals by interpolation trigonometric polynomials

Anatoly Serdyuk, Tetiana Stepaniuk

In this paper we establish asymptotically best possible interpolation Lebesgue-type inequalities for $2 π$ -periodic functions $f$ , which are representable as generalized Poisson int…

math.CA2023

Uniform approximations by Fourier sums on the sets of convolutions of periodic functions of high smoothness

Anatoly Serdyuk, Tetiana Stepaniuk

On the sets of $2 π$ -periodic functions $f$ , which are defined with a help of $(ψ, β)$ -integrals of the functions $φ$ from $L_{1}$ , we establish Lebesgue-type inequalities, in which…