A. Serdyuk

activity

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

collaborators

24 papers

math.CA2025

Estimates of deviations of Fourier sums on Weyl-Nagy classes $W_{β, 1}^{r}$

A. S. Serdyuk, I. V. Sokolenko

We establish estimates for exact upper bounds of deviations of partial Fourier sums $S_{n - 1} (f)$ on classes $W_{β, 1}^{r}, r > 2, β \in R,$ of $2 π$ -periodic functions whose $(r,β…

math.CA2024

Approximation by Fourier sums on the classes of generalized Poisson integrals

Anatoly Serdyuk, Tetiana Stepaniuk

We present a survey of results related to the solution of Kolmogorov--Nikolsky problem for Fourier sums on the classes of generalized Poisson integrals $C_{β, p}^{α, r}$ , which consi…

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…

math.CA2022

Approximation by Fourier sums in classes of Weyl--Nagy differentiable functions with high exponent of smoothness

A. S. Serdyuk, I. V. Sokolenko

We establish asymptotic estimates for the least upper bounds of approximations in the uniform metric by Fourier sums of order $n - 1$ of classes of $2 π$ -periodic Weyl--Nagy different…

math.CA2020★ 2 cited

About Lebesgue inequalities on the classes of generalized Poisson integrals

A. S. Serdyuk, T. A. Stepaniuk

For the functions $f$ , which can be represented in the form of the convolution $f(x)=\frac{a_{0}}{2}+\frac{1}π\int\limits_{-π}^π\sum\limits_{k=1}^{\infty}e^{-αk^{r}}\cos(kt-\frac{β…

math.CA2020

Uniform approximations by Fourier sums on classes of convolutions of periodic functions

A. S. Serdyuk, T. A. Stepanyuk

We establish asymptotic estimates for exact upper bounds of uniform approximations by Fourier sums on the classes of $2 π$ -periodic functions, which are represented by convolutions…

math.CA2019

Asymptotically best possible Lebesque-type inequalities for the Fourier sums on sets of generalized Poisson integrals

Anatoly Serdyuk, Tetiana Stepaniuk

In this paper we establish Lebesgue-type inequalities for $2 π$ -periodic functions $f$ , which are defined by generalized Poisson integrals of the functions $φ$ from $L_{p}$ , $1\leq…

math.CA2019★ 4 cited

Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothness

A. S. Serdyuk, I. V. Sokolenko

We find asymptotic equalities for the exact upper bounds of approximations by Fourier sums of Weyl-Nagy classes $W_{β, p}^{r}, 1 \leq p \leq \infty,$ for rapidly growing exponents of smoot…

math.CA2018

Lebesque-type inequalities for the Fourier sums on classes of generalized Poisson integrals

Anatoly Serdyuk, Tetiana Stepaniuk

For functions from the set of generalized Poisson integrals $C_{β}^{α, r} L_{p}$ , $1 \leq p < \infty$ , we obtain upper estimates for the deviations of Fourier sums in the uniform metric…

math.CA2015

Estimates for approximations by Fourier sums, best approximations and best orthogonal trigonometric approximations of the classes of (ψ, β)-differentiable functions

A. S. Serdyuk, T. A. Stepaniuk

We obtain the exact-order estimates for approximations by Fourier sums, best approximations and best orthogonal trigonometric approximations in metrics of spaces L_s, 1\leq s<\inft…

math.CA2014

Estimates of best $m$ -term trigonometric approximation of classes of analytic functions

A. S. Serdyuk, T. A. Stepaniuk

In metric of spaces $L_{s}, 1 \leq s \leq \infty$ , we obtain exact in order estimates of best $m$ -term trigonometric approximations of classes of convolutions of periodic functions,…

math.CA2014

Order estimates of the best orthogonal trigonometric approximations of classes of convolutions of periodic functions of not high smoothness

A. S. Serdyuk, T. A. Stepaniuk

We obtain order estimates for the best uniform orthogonal trigonometric approximations of $2 π$ -periodic functions, whose $(ψ, β)$ -derivatives belong to unit balls of spaces $L_{p},…

math.CA2014

Exact values of Kolmogorov widths of classes of analytic functions

A. S. Serdyuk, V. V. Bodenchuk

We prove that kernels of analytic functions of kind $H_{h, β} (t) = k = 1 \sum \infty \frac{1}{c o s h k h} cos (k t - \frac{β π}{2})$ , $h > 0$ , $β \in R$ , satisfies Kus…

math.CA2014★ 1 cited

Order estimates of the best approximations and approximations of Fourier sums of classes of convolutions of periodic functions of not high smoothness in uniform metric

A. S. Serdyuk, T. A. Stepaniuk

We obtain exact for order estimates of best uniform approximations and uniform approximations by Fourier sums of classes of convolutions the periodic functions belong to unit balls…

math.CA2013

Lower bounds for Kolmogorov widths of classes of Poisson integrals

A. S. Serdyuk, V. V. Bodenchuk

We expand the ranges of permissible values of $n$ ( $n \in N$ ) for which Poisson kernels $P_{q, β} (t) = k = 1 \sum \infty q^{k} cos (k t - \frac{β π}{2})$ , ${q\in(0…

math.CA2013

Order estimations of the best approximations and approximations of the Fourier sums on the classes of infinitely differentiable functions

A. S. Serdyuk, T. A. Stepaniuk

We obtained order estimations for the best uniform approximations by trigonometric polynomials and approximations by Fourier sums of classes of $2 π$ -periodic continuous functions,…

math.CA2013

Approximation by linear methods of classes of $(ψ, β ˉ) -$ differentiable functions

A. S. Serdyuk, I. V. Sokolenko

We calculate the least upper bounds for approximations in the metric of the space $L_{2}$ by linear methods of summation of Fourier series on classes of periodic functions $L^ψ_{\bar…

math.CA2013

Order estimation of the best approximations and of the approximations by Fourier sums of classes of $(ψ, β)$ --diferentiable functions

A. S. Serdyuk, U. Z. Grabova

There were established the exact-order estimations of the best uniform approximations byψ the trigonometrical polynoms on the $C_{β, p}^{ψ}$ classes of $2 π$ -periodic continuous functi…

math.CA2012★ 2 cited

Uniform approximation of periodical functions by trigonometric sums of a special type

A. S. Serdyuk, Ie. Yu. Ovsii

The approximation properties of the trigonometric sums U_{n,p}^ψof a special type are investigated on the classes C^ψ_{β, \infty} of (ψ,β)-differentiable (in the sense of Stepanets…

math.CA2012

Lebesgue-type inequalities for de la Vallee Poussin sums on the sets of analytic and entire functions

A. S. Serdyuk, A. P. Musienko

For the functions from sets $C_{β}^{ψ} C$ and $C_{β}^{ψ} L_{s}, 1 \leq s \leq \infty$ , generated by sequences $ψ (k) > 0$ satisfying the condition d'Alembert $\mathop {\rm \lim}\limits_{k\rightarr…

math.CA2011★ 7 cited

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

A. S. Serdyuk, Ie. Yu. Ovsii, A. P. Musienko

In this paper asymptotic equalities are found for the least upper bounds of deviations in the uniform metric of de la Vallee Poussin sums on classes of 2π-periodic (ψ,β)-differenti…

Estimates of deviations of Fourier sums on Weyl-Nagy classes Wβ,1r​

Approximation by Fourier sums on the classes of generalized Poisson integrals

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

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

Approximation of generalized Poisson integrals by interpolation trigonometric polynomials

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

Approximation by Fourier sums in classes of Weyl--Nagy differentiable functions with high exponent of smoothness

About Lebesgue inequalities on the classes of generalized Poisson integrals

Uniform approximations by Fourier sums on classes of convolutions of periodic functions

Asymptotically best possible Lebesque-type inequalities for the Fourier sums on sets of generalized Poisson integrals

Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothness

Lebesque-type inequalities for the Fourier sums on classes of generalized Poisson integrals

Estimates for approximations by Fourier sums, best approximations and best orthogonal trigonometric approximations of the classes of (ψ, β)-differentiable functions

Estimates of best m-term trigonometric approximation of classes of analytic functions

Order estimates of the best orthogonal trigonometric approximations of classes of convolutions of periodic functions of not high smoothness

Exact values of Kolmogorov widths of classes of analytic functions

Order estimates of the best approximations and approximations of Fourier sums of classes of convolutions of periodic functions of not high smoothness in uniform metric

Lower bounds for Kolmogorov widths of classes of Poisson integrals

Order estimations of the best approximations and approximations of the Fourier sums on the classes of infinitely differentiable functions

Approximation by linear methods of classes of (ψ,βˉ​)−differentiable functions

Order estimation of the best approximations and of the approximations by Fourier sums of classes of (ψ,β)--diferentiable functions

Uniform approximation of periodical functions by trigonometric sums of a special type

Lebesgue-type inequalities for de la Vallee Poussin sums on the sets of analytic and entire functions

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

Estimates of deviations of Fourier sums on Weyl-Nagy classes $W_{β, 1}^{r}$

Estimates of best $m$ -term trigonometric approximation of classes of analytic functions

Approximation by linear methods of classes of $(ψ, β ˉ) -$ differentiable functions

Order estimation of the best approximations and of the approximations by Fourier sums of classes of $(ψ, β)$ --diferentiable functions