Igor Sokolenko
@imath.kiev.ua
Institute of Mathematics of NAS of Ukraine
RESEARCH, TEACHING, or OTHER INTERESTS
Analysis
11
Scopus Publications
126
Scholar Citations
7
Scholar h-index
4
Scholar i10-index
Scopus Publications
- Asymptotic estimates for the widths of classes of functions of high smothness
A.S. Serdyuk and I.V. Sokolenko
Vasyl Stefanyk Precarpathian National University
We find two-sided estimates for Kolmogorov, Bernstein, linear and projection widths of the classes of convolutions of $2\\pi$-periodic functions $\\varphi$, such that $\\|\\varphi\\|_2\\le1$, with fixed generated kernels $\\Psi_{\\bar{\\beta}}$, which have Fourier series of the form $$\\sum\\limits_{k=1}^\\infty \\psi(k)\\cos(kt-\\beta_k\\pi/2),$$ where $\\psi(k)\\ge0,$ $\\sum\\psi^2(k)<\\infty, \\beta_k\\in\\mathbb{R}$. It is shown that for rapidly decreasing sequences $\\psi(k)$ (in particular, if $\\lim\\limits_{k\\rightarrow\\infty}{\\psi(k+1)}/{\\psi(k)}=0$) the obtained estimates are asymptotic equalities. We establish that asymptotic equalities for widths of this classes are realized by trigonometric Fourier sums. - Approximation by Fourier Sums in the Classes of Weyl–Nagy Differentiable Functions with High Exponent of Smoothness
A. S. Serdyuk and I. V. Sokolenko
Springer Science and Business Media LLC - Asymptotic Estimates for the Best Uniform Approximations of Classes of Convolution of Periodic Functions of High Smoothness
Anatolii S. Serdyuk and Igor V. Sokolenko
Springer Science and Business Media LLC - Correction to: Approximation by Interpolation Trigonometric Polynomials in Metrics of the Space L<inf>p</inf> on the Classes of Periodic Entire Functions (Ukrainian Mathematical Journal, (2019), 71, 2, (322-332), 10.1007/s11253-019-01647-2)
A. S. Serdyuk and I. V. Sokolenko
Springer Science and Business Media LLC - Approximation by Interpolation Trigonometric Polynomials in Metrics of the Space L<inf>p</inf> on the Classes of Periodic Entire Functions<sup>*</sup>
A. S. Serdyuk and I. V. Sokolenko
Springer Science and Business Media LLC - Approximation by fourier sums in classes of differentiable functions with high exponents of smoothness
- Asymptotic equalities for best approximations for classes of infinitely differentiable functions defined by the modulus of continuity
A. S. Serdyuk and I. V. Sokolenko
Pleiades Publishing Ltd - Asymptotic behavior of best approximations of classes of Poisson integrals of functions from Hω
A.S. Serdyuk and I.V. Sokolenko
Elsevier BV - Linear approximation methods and the best approximations of the Poisson integrals of functions from the classes H<inf>Ω p</inf> in the metrics of the spaces L<inf>p</inf>
A. S. Serdyuk and I. V. Sokolenko
Springer Science and Business Media LLC - Approximation of ψ̄-integrals of continuous functions defined on the real axis by Fourier operators
I. V. Sokolenko
Springer Science and Business Media LLC - Approximation of the ψ̄-integrals of functions defined on the real axis by fourier operators
O. I. Stepanets’ and I. V. Sokolenko
Springer Science and Business Media LLC
RECENT SCHOLAR PUBLICATIONS
- Владислав Федорович Бабенко (до 75-річчя від дня народження)
VP Motorny, IO Shevchuk, SB Vakarchuk, AO Korenovskyi, VO Kofanov, ...
Ukrains’ kyi Matematychnyi Zhurnal 76 (10), 1565-1568 2024 - Uniform approximation by Fourier sums in Weyl–Nagy Uniform approximation by Fourier sums in Weyl–Nagy classes W
A Serdyuk, I Sokolenko
2024 - До 100-річчя Майора Пилиповича Тімана (30.08. 1923–19.09. 2019)
OM Timokha, VP Motornyi, IO Shevchuk, SB Vakarchuk, PV Zaderei, ...
Ukrains’ kyi Matematychnyi Zhurnal 75 (8), 1149-1152 2023 - Asymptotic behavior of the widths of classes of the generalized Poisson integrals
A Serdyuk, I Sokolenko
Algebraic and Geometric Methods of Analysis, 102 2023 - Asymptotic estimates for the widths of classes of functions of high smoothness
AS Serdyuk, IV Sokolenko
arXiv preprint arXiv:2304.04586 2023 - Мiжнародна конференцiя „теорiя наближення функцiй та її застосування”, присвячена 80-рiччю вiд дня народження члена-кореспондента НАН України, професора ОІ Степанця (1942–2007)
I Sokolenko
Ukrains’ kyi Matematychnyi Zhurnal 74 (11), 1583-1584 2022 - OLEKSANDR IVANOVYCH STEPANETS (on his 80th birthday)
IO Lukovs' kyi, VL Makarov, OM Tymokha, VP Motornyi, IO Shevchuk, ...
UKRAINIAN MATHEMATICAL JOURNAL 74 (5), 661-663 2022 - Approximation by Fourier sums in the classes of Weyl–Nagy differentiable functions with high exponent of smoothness
AS Serdyuk, IV Sokolenko
Ukrainian Mathematical Journal 74 (5), 783-800 2022 - Наближення сумами Фур’є на класах диференційовних у сенсі Вейля–Надя функцій із високим показником гладкості
AS Serdyuk, IV Sokolenko
Ukrains’ kyi Matematychnyi Zhurnal 74 (5), 685-700 2022 - On asymptotic equations for the widths of classes of the generalized Poisson integrals
A Serdyuk, I Sokolenko
2021 - Asymptotic estimates for the widths of classes of periodic functions of high smothness
A Serdyuk, I Sokolenko
2021 - Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothness
AS Serdyuk, IV Sokolenko
Journal of Mathematical Sciences 252, 526-540 2021 - Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothness
AS Serdyuk, IV Sokolenko
arXiv preprint arXiv:2008.01450 2020 - Approximation by Interpolation Trigonometric Polynomials in Metrics of the Space Lp on the Classes of Periodic Entire Functions*
AS Serdyuk, IV Sokolenko
Ukrainian Mathematical Journal 71 (2), 322-332 2019 - Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothness
AS Serdyuk, IV Sokolenko
arXiv preprint arXiv:1906.02531 2019 - Наближення інтерполяційними тригонометричними поліно- мами в метриках просторів на класах періодичних цілих функцій
AS Serdyuk, IV Sokolenko
Ukrains’ kyi Matematychnyi Zhurnal 71 (2), 283-292 2019 - Approximation by Fourier sums and interpolation trigonometric polynomials in classes of differentiable functions with high exponents of smoothness
AS Serdyuk, IV Sokolenko
2019 - ОЛЕКСАНДР ІВАНОВИЧ СТЕПАНЕЦЬ (до 75-річчя від дня народження)
AS Romanyuk, VS Romanyuk, VV Savchuk, AM Samoilenko, AS Serdyuk, ...
Ukrains’ kyi Matematychnyi Zhurnal 69 (5), 579-579 2017 - Approximation of classes of convolutions of periodic functions by linear methods constructed on basis of Fourier-Lagrange coefficients
AS Serdyuk, IV Sokolenko
arXiv preprint arXiv:1703.09048 2017 - Asymptotic equalities for best approximations for classes of infinitely differentiable functions defined by the modulus of continuity
AS Serdyuk, IV Sokolenko
Mathematical Notes 99, 901-915 2016
MOST CITED SCHOLAR PUBLICATIONS
- Соколенко IВ Рiвномiрнi наближення класiв (ψ, β)-диференцiйовних функцiй лiнiйними методами
АС Сердюк
Теорiя наближення функцiй та сумiжнi питання: Зб. праць Iн-ту математики НАН 2011
Citations: 18 - Uniform approximation of the classes of (ψ, β)-differentiable functions by linear methods. Extremal Problems of the Theory of Functions and Related Problems
AS Serdyuk, IV Sokolenko
Proc. Inst. Math. NAS Ukr 8 (1), 181-189 2011
Citations: 18 - Asymptotic behavior of best approximations of classes of Poisson integrals of functions from Hω
AS Serdyuk, IV Sokolenko
Journal of Approximation Theory 163 (11), 1692-1706 2011
Citations: 17 - Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothness
AS Serdyuk, IV Sokolenko
arXiv preprint arXiv:1906.02531 2019
Citations: 14 - Asymptotic behavior of best approximations of classes of periodic analytic functions defined by moduli of continuity
AS Serdyuk, IV Sokolenko
Proc. of the Bulgarian–Turkish–Ukrainian Sci. Conf.“Mathematical Analysis 2010
Citations: 9 - Approximation by Interpolation Trigonometric Polynomials in Metrics of the Space Lp on the Classes of Periodic Entire Functions*
AS Serdyuk, IV Sokolenko
Ukrainian Mathematical Journal 71 (2), 322-332 2019
Citations: 8 - Approximation by of classes of (ψ, β)–differentiable functions by interpolation trigonometric polynomials, Zb
AS Serdyuk, IV Sokolenko
Pr. Inst. Mat. NAN Ukr 13, 289-299
Citations: 8 - Approximation by linear methods of classes of differentiable functions
AS Serdyuk, IV Sokolenko
arXiv preprint arXiv:1303.1300 2013
Citations: 7 - Approximation by Fourier sums in the classes of Weyl–Nagy differentiable functions with high exponent of smoothness
AS Serdyuk, IV Sokolenko
Ukrainian Mathematical Journal 74 (5), 783-800 2022
Citations: 6 - Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothness
AS Serdyuk, IV Sokolenko
Journal of Mathematical Sciences 252, 526-540 2021
Citations: 4 - Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothness
AS Serdyuk, IV Sokolenko
arXiv preprint arXiv:2008.01450 2020
Citations: 4 - Наближення сумами Фур’є на класах диференційовних у сенсі Вейля–Надя функцій із високим показником гладкості
AS Serdyuk, IV Sokolenko
Ukrains’ kyi Matematychnyi Zhurnal 74 (5), 685-700 2022
Citations: 3 - Asymptotic equalities for best approximations for classes of infinitely differentiable functions defined by the modulus of continuity
AS Serdyuk, IV Sokolenko
Mathematical Notes 99, 901-915 2016
Citations: 3 - The best approximation of Poisson integrals of functions from the class Hω
AS Serdyuk, IV Sokolenko
Dopov. Nats. Akad. Nauk Ukr 2, 33-37 2010
Citations: 3 - Linear approximation methods and the best approximations of the Poisson integrals of functions from the classes in the metrics of the spaces L p
AS Serdyuk, IV Sokolenko
Ukrainian Mathematical Journal 62 (7), 1139-1157 2010
Citations: 2 - Approximation of classes of convolutions of periodic functions by linear methods constructed on basis of Fourier-Lagrange coefficients
AS Serdyuk, IV Sokolenko
arXiv preprint arXiv:1703.09048 2017
Citations: 1 - Approximation of the-integrals of functions defined on the real axis by Fourier operators
OI Stepanets’, IV Sokolenko
Ukrainian Mathematical Journal 56 (7), 1144-1150 2004
Citations: 1