Serdyuk Anatolii
Publications
Serdyuk A., Sokolenko I. Asymptotic Estimates for the Widths of Classes of Functions of High Smothness. Carpathian Math. Publ. 2023, 15 (1), 246-259., https://doi.org/10.15330/cmp.15.1.246-259
Timokha, O. M., V. P. Motornyi, I. O. Shevchuk, S. B. Vakarchuk, P. V. Zaderei, V. O. Kofanov, N. V. Parfinovych, A. S. Romanyuk, A. S. Serdyuk, and I. V. Sokolenko. “On the 100th Birthday of Major Pylypovych Timan (30.08.1923 – 19.09.2019)”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 8, Aug. 2023, pp. 1149 -52, https://doi:10.3842/umzh.v75i8.7677.
Serdyuk, A., and T. Stepaniuk. “Approximation of Generalized Poisson Integrals by Interpolating Trigonometric Polynomials”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 7, July 2023, pp. 946 - 969, https://doi:10.37863/umzh.v75i7.7523.
Serdyuk, A., and T. Stepaniuk. “Uniform Approximations by Fourier Sums on the Sets of Convolutions of Periodic Functions of High Smoothness”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 4, May 2023, pp. 542 -67, https://doi:10.37863/umzh.v75i4.7411.
Lukovsky , I.A., Makarov , V.L., Perestyuk , M.O., Timokha , A.M., Boichuk , O.A., Gutlyanskii , V.Y., Kochubey , A.N., Motorny , V.P., Golub , A.P., Dzyubenko, G.A., Kovtunets , V.V., Nesterenko , O.N., Romanyuk , A.S., Serdyuk , A.S. and Torbin , G.M. 2022. Ihor Oleksandrovych Shevchuk (on his 75th birthday). Ukrains’kyi Matematychnyi Zhurnal. 74, 4 (May 2022), 439 - 442. DOI:https://doi.org/10.37863/umzh.v74i4.7139.PDF
O.I. Lukovskyi, V.L. Makarov, O.M. Timokha, V.P. Motorniy, I.O. Shevchuk, A.P. Golub, P.V. Zaderei, A.S. Romanyuk, V.V. Savchuk A.S. Serdyuk, I.V. Sokolenko, A.L. Shidlich. Oleksandr Ivanovych Stepanets’ (on his 80th birthday). Ukrains’kyi Matematychnyi Zhurnal. 74, 5 (Jun. 2022), 579 - 581. DOI:https://doi.org/10.37863/umzh.v74i5.7218.PDF
Serdyuk, A. S., and I. V. Sokolenko. “Approximation by Fourier Sums in Classes of Weyl – Nagy Differentiable Functions With High Exponent of Smoothness”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, no. 5, June 2022, pp. 685 -700. https://doi.org/10.37863/umzh.v74i5.7136
O.M. Tymoha, A.S. Romanyuk, A.S. Serdyuk, I.V. Sokolenko, A.L. Shidlich. International conference “Theory of approximation of functions and its applications” on the occasion of the 80th birthday of the corresponding member of the National Academy of Sciences of Ukraine, Professor O. I. Stepanets (1942-2007). Ukrains’kyi Matematychnyi Zhurnal. 74, 11 (Dec. 2022), 1583 - 1584. DOI:https://doi.org/10.37863/umzh.v74i11.7319.
Serdyuk A.S. , T. A. Stepanyuk T.A. About Lebesgue inequalities on the classes of generalized Poisson integrals //Jaen J. Approx. 12 (2021), 25–40.
http://www.ujaen.es/revista/jja/pdf/pre/jja-0012-01-21-2.pdf
Serdyuk, A. S.; Shydlich, A. L.
Problems of approximation theory in abstract linear spaces. (Ukrainian.English summary) // Zb. Pr. Inst. Mat. NAN Ukr. 18, No. 1, 594-643 (2021)
https://www.zbmath.org/pdf/07402552.pdf PDF
AbdullayevF., SerdyukA., and ShidlichA. Widths of Functional Classes Defined by Majorants of Generalized Moduli of Smoothness in the Spaces Sp // Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 6, June 2021, pp. 723 -7, https://doi.org/10.37863/umzh.v73i6.6432 Q-2
Serdyuk A.S., Hrabova U.Z. Order estimates of the uniform approximations by Zygmund sums on the classes of convolutions of periodic function // Carpathian Math. Publ.– 2021. – 13, ¹1. – pp. 68–80. Q-2
https://doi:10.15330/cmp.13.1.68-80 PDF
Anatolii S. Serdyuk, Igor V. Sokolenko. Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothness // Ukrainian Mathematical Bulletin. 2020.– 17, ¹3.– C. 396 – 413. Q-4 article
Samoilenko A. M., BabenkoV. F., Vakarchuk S. B., Velykin V. L., Davydov O. V., Kofanov V. O., Parfinovych N. V., Pas’ko A. M., Romanyuk A. S., Romanyuk V. S., Serdyuk A. S., Trigub R. M., Shevchuk I. O., and Shumeiko O. Î. “Vitalii Pavlovych Motornyi (on His 80th Birthday)”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 7, July 2020, pp. 1006-10, https://doi.org/10.37863/umzh.v72i7.6166PDF
Samoilenko A.Ì., Romanyuk A.S., Serdyuk A.S. An outstanding figure in the XX century approximation theory To the 100th anniversary of Academician of NAS of Ukraine N.P. Korneichuk//Visn. Nac. Akad. Nauk Ukr. – 2020, ¹1.— P.67 -72.PDF
A.M.Samoylenko, I.O.Lukovs’kyi, V.L.Makarov, V.P.Motornyi, V.F.Babenko, S.B.Vakarchuk, V.O.Kofanov, N.V.Parfinovych, A.S.Romanyuk, V.S.Romanyuk, A.S.Serdyuk, I.O.Shevchuk. Mykola Pavlovych Korneichuk (on His 100th Birthday)// Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 1, Jan. 2020, pp. 130-134, http://umj.imath.kiev.ua/index.php/umj/article/view/2331. PDF
Serdyuk, A. S., Sokolenko, I. V. Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothness //Methods of Functional Analysis and Topology.Vol. 25 (2019), no. 4, pp. – 381-387. Q-4 https://doi.org/10.1007/s11253-019-01647-2PDF
Samoilenko A. M., Zadiraka V. K. Letychevs’kyi O. A., Lukovsky I. O., Makarov Golub A. P., V. L.,Dzyadyk Yu. V., Kovtunets V. V., Romanyuk A. S., Serdyuk A. S., Shevchuk I. A., Zadiraka V. K. Vladyslav Kyrylovych Dzyadyk (on his 100th birthday) \\ Ukr. Mat. Zh. - 2019. - 71, ¹ 2. - pp. 147-150.PDF
Serdyuk, A. S., Sokolenko, I. V. Approximation by interpolation trigonometric polynomials in the metrics of Lp spaces on classes of periodic integer functions //Ukrainian Mathematical Journal, Vol. 71, no 2 (2019), 283 – 292. Q-2 https://doi.org/10.1007/s11253-019-01681-0 DOI
Serdyuk A. S., Stepanyuk T. A. Uniform Approximations by Fourier Sums in Classes of Generalized Poisson Integrals // Analysis Math., 45 (1) (2019), 201–236. Q-2 https://doi.org/10.1007/s10476-018-0310-1 DOI
A.M.Samoylenko, F.H.Abdullayev, V.V.Savchuk, A.S.Serdyuk, V.V.Savchuk.International conference on the mathematical analysis, differential equations, and their applications (MADEA-8) devoted to the 80th birthday of Academician A. M. Samoilenko // Óêð. ìàò. æóðí. - 2018. - 70, ¹ 10. - P. 1439-1440. PDF
Serdyuk A. S., Stepanyuk T. A. LEBESGUE-TYPE INEQUALITIES FOR THE FOURIER SUMS ON CLASSES OF GENERALIZED POISSON INTEGRALS // Bulletin de la societe des sciences et des lettres de Lodz, vol. 68, ¹ 2 (2018), P 45-52.DOI: 10.26485/0459-6854/2018/68.2/4 DOI
Samoilenko, A.M.; Lukovs’kyi, I.O.; Makarov, V.L.; Motornyi, V.P., Zaderei, P.V.; Romanyuk, A.S.; Golub À.P.; Serdyuk, A.S.; Savchuk V.V.; Romanyuk, V.S.; Sokolenko, I. V.; Shydlich, A.L. Oleksandr Ivanovych Stepanets’ (on his 75th birthday) // Ukr. Mat. Zh. - 2017. - 69, ¹ 5. - P. 579-581. PDF
Serdyuk A. S., Stepanyuk T. A. Approximation of the classes of generalized Poisson integrals by Fourier sums in metrics of the spaces Ls // Ukr. Mat. Zh. - 2017. - 69, ¹ 5. - pp. 695-704. Q-3 https://doi.org/10.1007/s11253-017-1397-4PDF
Serdyuk A.S. On optimal subspaces for Kolmogorov widths of classes of 2π-periodic analytic functions // Bulletin: de la societe des sciences et des letters de Lodz, vol. 67, ¹ 1 (2017). DOI: https://doi.org/10.26485/0459-6854/2017/67.1/3PDF
Serdyuk, A. S.; Sokolenko, I. V. Approximation of classes of convolutions of periodic functions by linear methods constructed on basis of Fourier-Lagrange coefficients// Analysis and application/ (Ukrainian) Zb. Pr. Inst. Mat. NAN Ukr. 14, No. 1, 238-248 (2017). PDF
Serdyuk, A. S.; Sokolenko, I. V. Asymptotic equalities for best approximations for classes of infinitely differentiable functions defined by the modulus of continuity. (Russian) Mat. Zametki 99 (2016), no. 6, 904--920; translation in Math. Notes 99 (2016), no. 5-6, 901–915 Q-2 https://doi.org/10.1134/S0001434616050291PDF
Serdyuk, A. S.; Sokolenko, I. V. Approximation by of classes of (ψ,β¯)-differentiable functions by interpolation trigonometric polynomials// Zb. Pr. Inst. Mat. NAN Ukr. 13, No. 1, 289-299 (2016). PDF
A.S. Serdyuk and T.A. Stepanyuk, Estimates for approximations by Fourier sums, best approximations and best orthogonal trigonometric approximations of the classes of (ψ,β)-differentiable functions, Bulletin: de la societe des sciences et des letters de Lodz, vol. 66, No 2 (2016). http://79.96.70.35/ltn/images/bull%2066-2-2016_full.pdfPDF
Serdyuk A.S., Stepanyuk T.A . Uniform approximations by Fourier sums on the classes of convolutions with generalized Poisson kernels (Ukrainian)// Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky. – 2016, No. 11, 10-16. https://doi.org/10.15407/dopovidi2016.11.010 PDF
Serdyuk, A.S.; Stepanyuk, T.A. Order estimates of the best orthogonal trigonometric approximations of classes of convolutions of periodic functions of not high smoothness // Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky, No. 7, 13-19 (2015).
Bodenchuk, V.V.,Serdyuk, A.S. Exact values of Kolmogorov widths of classes of analytic functions II //Ukrainian Mathematical Journal, Vol. 67, no 8 (2015), 1011 –1018. Q-3 https://doi.org/10.1007/s11253-016-1141-5 PDF
Serdyuk, A.S.; Stepanyuk, T.A. Order estimates of the best orthogonal trigonometric approximations of classes of convolutions of periodic functions of not high smoothness //Ukrainian Mathematical Journal, Vol. 67, no 7 (2015), 916 – 936. PDF
Bodenchuk, V.V.,Serdyuk, A.S. Exact values of Kolmogorov widths of classes of analytic functions I //Ukrainian Mathematical Journal, Vol. 67, no 6 (2015), 719 – 738. PDF
Serdyuk, A.S.; Stepanyuk, T.A. Estimates of the best m-term trigonometric approximations of classes of analytic functions. (Ukrainian. English summary) //
Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky , No. 2, 32-37 (2015).
Serdyuk, A.S.; Stepanyuk, T.A. 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 // Ukrainian Mathematical Journal, Vol. 66, no 12 (2014), 1658–1675.
Serdyuk, A.S.; Stepanyuk, T.A.Estimations of the best approximations of classes of infinitely differentiable functions in uniform and integral metrics // Ukrainian Mathematical Journal, Vol. 66, no 9 (2014), 1244-1256
Serdyuk, A.S.; Ovsii, Ie.Yu.Uniform approximation of periodical functions by trigonometric sums of special type. ISRN Math. Anal. 2014, Article ID 165389, 11 p.
Serdyuk, A.S.; Stepanyuk, T.A.Order estimates for the best approximation and approximation by Fourier sums of classes of infinitely differentiable functions. (Ukrainian) Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 255-282 (2013).
Serdyuk, A.S.; Sokolenko, I.V. Approximation by linear methods of classes of (ψ,β ¯)-differentiable functions. (Ukrainian) Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 245-254 (2013).
Serdyuk, A.S.; Grabova, U.Z. Estimates of uniform approximations by Zygmund sums on classes of convolutions of periodic functions. (Ukrainian) Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 222-244 (2013).
Serdyuk, A.S.; Bodenchuk, V.V.Estimates from below for Kolmogorov widths in classes of Poisson integrals. (Ukrainian) Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 204-221 (2013).
Serdyuk, A.S.; Bodenchuk, V.V. Exact values of Kolmogorov widths of classes of Poisson integrals. (English) J. Approx. Theory 173, ¹ 9, 89-109 (2013).
Musienko, A.P.; Serdyuk, A.S. Lebesgue-type inequalities for the de la Vallée-Poussin sums on sets of entire functions. Ukr. Math. J. 65, No. 5, 709-722 (2013); translation from Ukr. Mat. Zh. 65, No. 5, 642-653 (2013).
Musienko, A.P.; Serdyuk, A.S. Lebesgue-type inequalities for the de la Valée-Poussin sums on sets of analytic functions. Ukr. Math. J. 65, No. 4, 575-592 (2013); translation from Ukr. Mat. Zh. 65, No. 4, 522-537 (2013).
Serdyuk, A.S.; Bodenchuk, V.V. Estimates for Kolmogorov widths of classes of Poisson integrals. (Ukrainian) Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2013, No. 5, 31-36 (2013).
A. S. Serdyuk, Ie. Yu. Ovsii, Uniform approximation of Poisson integrals of functions from the class H ω by de la Vallée Poussin sums. Analysis Mathematica. ${\bf 38}$ (2012), no. 4, 305-325.
A. S. Serdyuk, Ie. Yu. Ovsii and A. P. Musienko, Approximation of classes of analytic functions by de la Vallee Poussin sums in uniform metric. Rendiconti di Matematica. ${\bf 32}$ (2012), no. 1-2, 1-15.
Serdyuk A.S. Approximation by interpolation trigonometric polynomials on classes of periodic analytic functions. Ukr. Mat. Zh. 64 (2012), No.5, 698-712.
A.S. Serdyuk, I.V. Sokolenko. Uniform approximations of classes of (ψ,β¯)-differentiate functions by linear methods // Zb. Pr. Inst. Mat. NAN Ukr. 8, No. 1, 181-189 (2011).
Serdyuk, A. S., Sokolenko, I. V. Asymptotic behavior of best approximations of classes of Poisson integrals of functions from $H_\omega$. J. Approx. Theory 163 (2011), no. 11, 1692–1706.
Ovsii, E.Yu. and Serdyuk, A.S. Approximation of continuous periodic functions by de la Vallee Poussin sums. (Ukrainian. English summary) Zb. Pr. Inst. Mat. NAN Ukr. 8, No. 1 (2011).
A.S. Serdyuk, I.V. Sokolenko. Asymptotic behavior of best approximations of classes of Poisson integrals of functions from // Journal of Approximation Theory. - 2011. – 163, ¹ 11. – P. 1692-1706.
Serdyuk À.S., Sokolenko I.V. Asymptotic Behavior of Best approximations of Classes of Periodic Analitic Functions Defined by Moduli of Continuity // Bulgarian-Turkish-Ukrainian Scientific Conference "Mathematical Analysis, Differential Equations and their Applications", Sunny Beach, 15-20 September, 2010. – Sofia: Academic Publishing House "Prof. Marin Drinov", 2011. – P. 173–182.
Serdyuk A, Ovsii I. On the best approximation of certain classes of periodic functions by trigonometric polynomials // Azerbaijan Journal of Mathematics. - 2011. - 1, ¹1. – P.129–144.
Serdyuk A.S., Chaychenko S.O.Approximation of classes of analytic functions by special linear form // Ukr. Math. Zh. - 2011. - 63, ¹ 1. - C.102-109.
Serdyuk A.S. Approximation of Poisson integrals by de la Vallée-Poussin sums in uniform and integral metrics // Ukr. Mat. Zh. (2010) 62, No. 12, 1672-1686.
Serdyuk, A.S., Musienko, A.P. The Lebesgue type inequalities for the de la Vallée Poussin sums in approximation of Poisson integrals. (Ukrainian) //
Zb. Pr. Inst. Mat. NAN Ukr.(2010) 7, No. 1, 298-316 .
Serdyuk A.S., Vojtovych, V.A. Approximation of classes of entire functions by interpolation analogues of the de la Vallée Poussin sums. (Ukrainian) // Zb. Pr. Inst. Mat. NAN Ukr.(2010) 7, No. 1, 274-297.
Serdyuk A.S. Approximation of Poisson integrals Valle Poussin sums in uniform and integral metrics // Bulletin of the Slavonic State Pedagogical University.- Mathematics.-1, ¹ 4 .- Slavyansk: SSPU, 2010 .- C.107-127.
A.S. Serdyuk, I.V. Sokolenko, Linear approximation methods and the best approximations of the Poisson integrals of functions from the classes $H_{ω_p} $ in the metrics of the spaces Lp. (Ukrainian; English) Ukr. Mat. Zh. 62, No. 7, 979-996 (2010); translation in Ukr. Math. J. 62, No. 7, 1139-1157 (2010).
Serdyuk A.S., Sokolenko, I.V. The best approximation of Poisson integrals of functions from the class $H_\omega $. Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky, No. 2, 33-37 (2010).
Serdyuk A.S. Approximation of Poisson integrals by Valle'e-Poussinsums in uniform and integral metrics. Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky, No. 6, 34-39 (2009)
Serdyuk A.S., Ovsii E.Yu. Approximation of the classes $C_\beta^\psi H_\omega$ by generalized Zygmund sums. Ukr. Mat. Zh. 61 , No. 4, 524-537 (2009).
Stepanets A.I., Serdyuk, A.S., Shidlich, A.L. Classification of infinitely differentiable periodic functions. Ukr. Mat. Zh. 60, No. 12, 1686-1708 (2008).
Serdyuk A.S. Approximation of Poisson integrals by one linear approximation method in uniform and integral metrics. Ukr. Mat. Zh. 60, No. 7, 976-982 (2008).
Stepanets' O.I., Serdyuk A.S., Shydlich, A.L. On some new criteria of infinite differentiability of periodic functions. Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky, No. 1, 22-26 (2008).
Stepanets' O.I., Serdyuk A.S., Shydlich A.L. On some new criteria of infinite differentiability of periodic functions. Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky, No. 1, 22-26 (2008).
Stepanets' O.I., Serdyuk A.S., Shydlich A.L. On some new criteria for infinite differentiability of periodic functions. Ukr. Mat. Zh. 59, No. 10, 1399-1409 (2007)
Stepanets' O.I., Serdyuk A.S., Shydlich A.L. On some new criteria of infinite differentiability of periodic functions. Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky, No. 1, 22-26 (2008).
Serdyuk A.S. Approximation of classes of analytic functions by Fourier sums in the metric of the space $L_p$. Ukr. Mat. Zh. 57, No. 10, 1395-1408 (2005).
Serdyuk A.S. Approximation of classes of analytic functions by Fourier sums in the uniform metric. Ukr. Mat. Zh. 57, No. 8, 1079-1096 (2005).
Voitsekhivs’kyj, V. R.; Serdyuk, A. S. Jackson type inequalities in approximation of functions from the Sp space by the Voronoi method.(Ukrainian)
Zb. Pr. Inst. Mat. NAN Ukr. 2, No. 2, 43-53 (2005).
Serdyuk A.S. Best approximations and widths of classes of convolutions of periodic functions of high smoothness. Ukr. Mat. Zh. 57, No. 7, 946-971 (2005).
Serdyuk A.S. Approximation of Poisson integrals by de la Vall\'ee Poussin sums. Ukr. Mat. Zh. 56, No. 1, 97-107 (2004).
Serdyuk A.S. Widths in the space Sp of classes of functions defined by the moduli of continuity of their ψ-derivatives. - Extremal Problems in the Theory of Functions and Related Problems: Proceedings of the Institute of Mathematics of NAS of Ukraine. – 2003. – 46. – P. 229–248.
Stepanets A.I. Serdyuk A.S. Direct and indirect theorems of theory of function approximation in the space $S^p$. Ukr. Mat. Zh. 54, No.1,
106-124 (2002).
Serdyuk A.S. Approximation of periodic analytic functions by trigonometric interpolation polynomials in the metric of the space $L$. Ukr. Mat. Zh. 54, No.5, 692-699 (2002).
Serdyuk A.S. Approximation of infinitely differentiable periodic functions by trigonometric interpolation polynomials in integral metric. Ukr. Mat. Zh. 53, No 12, 1654-1663 (2001).
Stepanets A.I., Serdyuk A.S. Approximation of periodic analytic functions by interpolation trigonometric polynomials. Ukr. Mat. Zh. 52, No.12, 1689-1701 (2000).
Stepanets A.I., Serdyuk A.S. Approximation of periodic analytic functions by interpolation trigonometric polynomials. Ukr. Mat. Zh. 52, No.12, 1689-1701 (2000).
Serdyuk A.S. Approximation of periodic functions of high smoothness by interpolation trigonometric polynomials in the metric of $L_1$. Ukr. Mat. Zh. 52, No.7, 994-998 (2000).
Stepanets A.I., Serdyuk A.S. Lebesgue inequalities for Poisson integrals. Ukr. Mat. Zh. 52, No.6, 798-808 (2000).
Stepanets A.I., Serdyuk A.S. Approximations by Fourier sums and best approximations on classes of analytic functions. Ukr. Mat. Zh. 52, No.3, 375-395 (2000).
Stepanets A.I., Serdyuk A.S. Approximations of analytic functions by Fourier sums. Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky, No.12, 20-24 (2000).
Serdyuk A.S. On asymptotically exact error estimates for the approximation of functions of high smoothness by interpolating trigonometric polynomials. Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky, No.8, 29-33 (1999).
Serdyuk A.S. Widths and best approximations for classes of convolutions of periodic functions. Ukr. Mat. Zh. 51, No.5, 674-687 (1999).
Serdyuk A.S. On the existence and uniqueness of a solution of the problem of uniform $SK$-spline interpolation. Ukr. Mat. Zh. 51, No.4, 486-492 (1999).
Stepanets, A.I., Romanyuk, A.S. & Serdyuk, A.S. International conference on the theory of approximation of functions and its applications dedicated to the memory of V. K. Dzyadyk. Ukr Math J 51, 1459–1460 (1999).
doi
Serdyuk A.S. Estimates of the Kolmogorov width of classes of infinitely differentiable periodic functions. Ukr. Mat. Zh. 49, No.12, 1700-1706 (1997).
Serdyuk A.S. On the best approximation of classes of convolutions of periodic functions by trigonometric polynomials. Ukr. Mat. Zh. 47, No.9, 1261-1265 (1995).
Stepanets A.I., Serdyuk A.S. Lower bounds for widths classes of convolutions of periodic functions in $C$ and $L$ metric. Ukr. Mat. Zh. 47, No.8, 1112-1121 (1995).
Stepanets A.I., Serdyuk A.S. On the existence of interpolating $SK$-splines. Ukr. Mat. Zh. 46, No.11, 1546-1553 (1994).
Timokha, O. M., V. P. Motornyi, I. O. Shevchuk, S. B. Vakarchuk, P. V. Zaderei, V. O. Kofanov, N. V. Parfinovych, A. S. Romanyuk, A. S. Serdyuk, and I. V. Sokolenko. “On the 100th Birthday of Major Pylypovych Timan (30.08.1923 – 19.09.2019)”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 8, Aug. 2023, pp. 1149 -52, https://doi:10.3842/umzh.v75i8.7677.
Serdyuk, A., and T. Stepaniuk. “Approximation of Generalized Poisson Integrals by Interpolating Trigonometric Polynomials”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 7, July 2023, pp. 946 - 969, https://doi:10.37863/umzh.v75i7.7523.
Serdyuk, A., and T. Stepaniuk. “Uniform Approximations by Fourier Sums on the Sets of Convolutions of Periodic Functions of High Smoothness”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 4, May 2023, pp. 542 -67, https://doi:10.37863/umzh.v75i4.7411.
Lukovsky , I.A., Makarov , V.L., Perestyuk , M.O., Timokha , A.M., Boichuk , O.A., Gutlyanskii , V.Y., Kochubey , A.N., Motorny , V.P., Golub , A.P., Dzyubenko, G.A., Kovtunets , V.V., Nesterenko , O.N., Romanyuk , A.S., Serdyuk , A.S. and Torbin , G.M. 2022. Ihor Oleksandrovych Shevchuk (on his 75th birthday). Ukrains’kyi Matematychnyi Zhurnal. 74, 4 (May 2022), 439 - 442. DOI:https://doi.org/10.37863/umzh.v74i4.7139.PDF
O.I. Lukovskyi, V.L. Makarov, O.M. Timokha, V.P. Motorniy, I.O. Shevchuk, A.P. Golub, P.V. Zaderei, A.S. Romanyuk, V.V. Savchuk A.S. Serdyuk, I.V. Sokolenko, A.L. Shidlich. Oleksandr Ivanovych Stepanets’ (on his 80th birthday). Ukrains’kyi Matematychnyi Zhurnal. 74, 5 (Jun. 2022), 579 - 581. DOI:https://doi.org/10.37863/umzh.v74i5.7218.PDF
Serdyuk, A. S., and I. V. Sokolenko. “Approximation by Fourier Sums in Classes of Weyl – Nagy Differentiable Functions With High Exponent of Smoothness”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, no. 5, June 2022, pp. 685 -700. https://doi.org/10.37863/umzh.v74i5.7136
O.M. Tymoha, A.S. Romanyuk, A.S. Serdyuk, I.V. Sokolenko, A.L. Shidlich. International conference “Theory of approximation of functions and its applications” on the occasion of the 80th birthday of the corresponding member of the National Academy of Sciences of Ukraine, Professor O. I. Stepanets (1942-2007). Ukrains’kyi Matematychnyi Zhurnal. 74, 11 (Dec. 2022), 1583 - 1584. DOI:https://doi.org/10.37863/umzh.v74i11.7319.
Serdyuk A.S. , T. A. Stepanyuk T.A. About Lebesgue inequalities on the classes of generalized Poisson integrals //Jaen J. Approx. 12 (2021), 25–40.
http://www.ujaen.es/revista/jja/pdf/pre/jja-0012-01-21-2.pdf
Serdyuk, A. S.; Shydlich, A. L.
Problems of approximation theory in abstract linear spaces. (Ukrainian.English summary) // Zb. Pr. Inst. Mat. NAN Ukr. 18, No. 1, 594-643 (2021)
https://www.zbmath.org/pdf/07402552.pdf PDF
AbdullayevF., SerdyukA., and ShidlichA. Widths of Functional Classes Defined by Majorants of Generalized Moduli of Smoothness in the Spaces Sp // Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 6, June 2021, pp. 723 -7, https://doi.org/10.37863/umzh.v73i6.6432 Q-2
Serdyuk A.S., Hrabova U.Z. Order estimates of the uniform approximations by Zygmund sums on the classes of convolutions of periodic function // Carpathian Math. Publ.– 2021. – 13, ¹1. – pp. 68–80. Q-2
https://doi:10.15330/cmp.13.1.68-80 PDF
Anatolii S. Serdyuk, Igor V. Sokolenko. Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothness // Ukrainian Mathematical Bulletin. 2020.– 17, ¹3.– C. 396 – 413. Q-4 article
Samoilenko A. M., BabenkoV. F., Vakarchuk S. B., Velykin V. L., Davydov O. V., Kofanov V. O., Parfinovych N. V., Pas’ko A. M., Romanyuk A. S., Romanyuk V. S., Serdyuk A. S., Trigub R. M., Shevchuk I. O., and Shumeiko O. Î. “Vitalii Pavlovych Motornyi (on His 80th Birthday)”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 7, July 2020, pp. 1006-10, https://doi.org/10.37863/umzh.v72i7.6166PDF
Samoilenko A.Ì., Romanyuk A.S., Serdyuk A.S. An outstanding figure in the XX century approximation theory To the 100th anniversary of Academician of NAS of Ukraine N.P. Korneichuk//Visn. Nac. Akad. Nauk Ukr. – 2020, ¹1.— P.67 -72.PDF
A.M.Samoylenko, I.O.Lukovs’kyi, V.L.Makarov, V.P.Motornyi, V.F.Babenko, S.B.Vakarchuk, V.O.Kofanov, N.V.Parfinovych, A.S.Romanyuk, V.S.Romanyuk, A.S.Serdyuk, I.O.Shevchuk. Mykola Pavlovych Korneichuk (on His 100th Birthday)// Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 1, Jan. 2020, pp. 130-134, http://umj.imath.kiev.ua/index.php/umj/article/view/2331. PDF
Serdyuk, A. S., Sokolenko, I. V. Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothness //Methods of Functional Analysis and Topology.Vol. 25 (2019), no. 4, pp. – 381-387. Q-4 https://doi.org/10.1007/s11253-019-01647-2PDF
Samoilenko A. M., Zadiraka V. K. Letychevs’kyi O. A., Lukovsky I. O., Makarov Golub A. P., V. L.,Dzyadyk Yu. V., Kovtunets V. V., Romanyuk A. S., Serdyuk A. S., Shevchuk I. A., Zadiraka V. K. Vladyslav Kyrylovych Dzyadyk (on his 100th birthday) \\ Ukr. Mat. Zh. - 2019. - 71, ¹ 2. - pp. 147-150.PDF
Serdyuk, A. S., Sokolenko, I. V. Approximation by interpolation trigonometric polynomials in the metrics of Lp spaces on classes of periodic integer functions //Ukrainian Mathematical Journal, Vol. 71, no 2 (2019), 283 – 292. Q-2 https://doi.org/10.1007/s11253-019-01681-0 DOI
Serdyuk A. S., Stepanyuk T. A. Uniform Approximations by Fourier Sums in Classes of Generalized Poisson Integrals // Analysis Math., 45 (1) (2019), 201–236. Q-2 https://doi.org/10.1007/s10476-018-0310-1 DOI
A.M.Samoylenko, F.H.Abdullayev, V.V.Savchuk, A.S.Serdyuk, V.V.Savchuk.International conference on the mathematical analysis, differential equations, and their applications (MADEA-8) devoted to the 80th birthday of Academician A. M. Samoilenko // Óêð. ìàò. æóðí. - 2018. - 70, ¹ 10. - P. 1439-1440. PDF
Serdyuk A. S., Stepanyuk T. A. LEBESGUE-TYPE INEQUALITIES FOR THE FOURIER SUMS ON CLASSES OF GENERALIZED POISSON INTEGRALS // Bulletin de la societe des sciences et des lettres de Lodz, vol. 68, ¹ 2 (2018), P 45-52.DOI: 10.26485/0459-6854/2018/68.2/4 DOI
Samoilenko, A.M.; Lukovs’kyi, I.O.; Makarov, V.L.; Motornyi, V.P., Zaderei, P.V.; Romanyuk, A.S.; Golub À.P.; Serdyuk, A.S.; Savchuk V.V.; Romanyuk, V.S.; Sokolenko, I. V.; Shydlich, A.L. Oleksandr Ivanovych Stepanets’ (on his 75th birthday) // Ukr. Mat. Zh. - 2017. - 69, ¹ 5. - P. 579-581. PDF
Serdyuk A. S., Stepanyuk T. A. Approximation of the classes of generalized Poisson integrals by Fourier sums in metrics of the spaces Ls // Ukr. Mat. Zh. - 2017. - 69, ¹ 5. - pp. 695-704. Q-3 https://doi.org/10.1007/s11253-017-1397-4PDF
Serdyuk A.S. On optimal subspaces for Kolmogorov widths of classes of 2π-periodic analytic functions // Bulletin: de la societe des sciences et des letters de Lodz, vol. 67, ¹ 1 (2017). DOI: https://doi.org/10.26485/0459-6854/2017/67.1/3PDF
Serdyuk, A. S.; Sokolenko, I. V. Approximation of classes of convolutions of periodic functions by linear methods constructed on basis of Fourier-Lagrange coefficients// Analysis and application/ (Ukrainian) Zb. Pr. Inst. Mat. NAN Ukr. 14, No. 1, 238-248 (2017). PDF
Serdyuk, A. S.; Sokolenko, I. V. Asymptotic equalities for best approximations for classes of infinitely differentiable functions defined by the modulus of continuity. (Russian) Mat. Zametki 99 (2016), no. 6, 904--920; translation in Math. Notes 99 (2016), no. 5-6, 901–915 Q-2 https://doi.org/10.1134/S0001434616050291PDF
Serdyuk, A. S.; Sokolenko, I. V. Approximation by of classes of (ψ,β¯)-differentiable functions by interpolation trigonometric polynomials// Zb. Pr. Inst. Mat. NAN Ukr. 13, No. 1, 289-299 (2016). PDF
A.S. Serdyuk and T.A. Stepanyuk, Estimates for approximations by Fourier sums, best approximations and best orthogonal trigonometric approximations of the classes of (ψ,β)-differentiable functions, Bulletin: de la societe des sciences et des letters de Lodz, vol. 66, No 2 (2016). http://79.96.70.35/ltn/images/bull%2066-2-2016_full.pdfPDF
Serdyuk A.S., Stepanyuk T.A . Uniform approximations by Fourier sums on the classes of convolutions with generalized Poisson kernels (Ukrainian)// Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky. – 2016, No. 11, 10-16. https://doi.org/10.15407/dopovidi2016.11.010 PDF
Serdyuk, A.S.; Stepanyuk, T.A. Order estimates of the best orthogonal trigonometric approximations of classes of convolutions of periodic functions of not high smoothness // Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky, No. 7, 13-19 (2015).
Bodenchuk, V.V.,Serdyuk, A.S. Exact values of Kolmogorov widths of classes of analytic functions II //Ukrainian Mathematical Journal, Vol. 67, no 8 (2015), 1011 –1018. Q-3 https://doi.org/10.1007/s11253-016-1141-5 PDF
Serdyuk, A.S.; Stepanyuk, T.A. Order estimates of the best orthogonal trigonometric approximations of classes of convolutions of periodic functions of not high smoothness //Ukrainian Mathematical Journal, Vol. 67, no 7 (2015), 916 – 936. PDF
Bodenchuk, V.V.,Serdyuk, A.S. Exact values of Kolmogorov widths of classes of analytic functions I //Ukrainian Mathematical Journal, Vol. 67, no 6 (2015), 719 – 738. PDF
Serdyuk, A.S.; Stepanyuk, T.A. Estimates of the best m-term trigonometric approximations of classes of analytic functions. (Ukrainian. English summary) //
Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky , No. 2, 32-37 (2015).
Serdyuk, A.S.; Stepanyuk, T.A. 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 // Ukrainian Mathematical Journal, Vol. 66, no 12 (2014), 1658–1675.
Serdyuk, A.S.; Stepanyuk, T.A.Estimations of the best approximations of classes of infinitely differentiable functions in uniform and integral metrics // Ukrainian Mathematical Journal, Vol. 66, no 9 (2014), 1244-1256
Serdyuk, A.S.; Ovsii, Ie.Yu.Uniform approximation of periodical functions by trigonometric sums of special type. ISRN Math. Anal. 2014, Article ID 165389, 11 p.
Serdyuk, A.S.; Stepanyuk, T.A.Order estimates for the best approximation and approximation by Fourier sums of classes of infinitely differentiable functions. (Ukrainian) Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 255-282 (2013).
Serdyuk, A.S.; Sokolenko, I.V. Approximation by linear methods of classes of (ψ,β ¯)-differentiable functions. (Ukrainian) Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 245-254 (2013).
Serdyuk, A.S.; Grabova, U.Z. Estimates of uniform approximations by Zygmund sums on classes of convolutions of periodic functions. (Ukrainian) Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 222-244 (2013).
Serdyuk, A.S.; Bodenchuk, V.V.Estimates from below for Kolmogorov widths in classes of Poisson integrals. (Ukrainian) Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 204-221 (2013).
Serdyuk, A.S.; Bodenchuk, V.V. Exact values of Kolmogorov widths of classes of Poisson integrals. (English) J. Approx. Theory 173, ¹ 9, 89-109 (2013).
Musienko, A.P.; Serdyuk, A.S. Lebesgue-type inequalities for the de la Vallée-Poussin sums on sets of entire functions. Ukr. Math. J. 65, No. 5, 709-722 (2013); translation from Ukr. Mat. Zh. 65, No. 5, 642-653 (2013).
Musienko, A.P.; Serdyuk, A.S. Lebesgue-type inequalities for the de la Valée-Poussin sums on sets of analytic functions. Ukr. Math. J. 65, No. 4, 575-592 (2013); translation from Ukr. Mat. Zh. 65, No. 4, 522-537 (2013).
Serdyuk, A.S.; Bodenchuk, V.V. Estimates for Kolmogorov widths of classes of Poisson integrals. (Ukrainian) Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2013, No. 5, 31-36 (2013).
A. S. Serdyuk, Ie. Yu. Ovsii, Uniform approximation of Poisson integrals of functions from the class H ω by de la Vallée Poussin sums. Analysis Mathematica. ${\bf 38}$ (2012), no. 4, 305-325.
A. S. Serdyuk, Ie. Yu. Ovsii and A. P. Musienko, Approximation of classes of analytic functions by de la Vallee Poussin sums in uniform metric. Rendiconti di Matematica. ${\bf 32}$ (2012), no. 1-2, 1-15.
Serdyuk A.S. Approximation by interpolation trigonometric polynomials on classes of periodic analytic functions. Ukr. Mat. Zh. 64 (2012), No.5, 698-712.
A.S. Serdyuk, I.V. Sokolenko. Uniform approximations of classes of (ψ,β¯)-differentiate functions by linear methods // Zb. Pr. Inst. Mat. NAN Ukr. 8, No. 1, 181-189 (2011).
Serdyuk, A. S., Sokolenko, I. V. Asymptotic behavior of best approximations of classes of Poisson integrals of functions from $H_\omega$. J. Approx. Theory 163 (2011), no. 11, 1692–1706.
Ovsii, E.Yu. and Serdyuk, A.S. Approximation of continuous periodic functions by de la Vallee Poussin sums. (Ukrainian. English summary) Zb. Pr. Inst. Mat. NAN Ukr. 8, No. 1 (2011).
A.S. Serdyuk, I.V. Sokolenko. Asymptotic behavior of best approximations of classes of Poisson integrals of functions from // Journal of Approximation Theory. - 2011. – 163, ¹ 11. – P. 1692-1706.
Serdyuk À.S., Sokolenko I.V. Asymptotic Behavior of Best approximations of Classes of Periodic Analitic Functions Defined by Moduli of Continuity // Bulgarian-Turkish-Ukrainian Scientific Conference "Mathematical Analysis, Differential Equations and their Applications", Sunny Beach, 15-20 September, 2010. – Sofia: Academic Publishing House "Prof. Marin Drinov", 2011. – P. 173–182.
Serdyuk A, Ovsii I. On the best approximation of certain classes of periodic functions by trigonometric polynomials // Azerbaijan Journal of Mathematics. - 2011. - 1, ¹1. – P.129–144.
Serdyuk A.S., Chaychenko S.O.Approximation of classes of analytic functions by special linear form // Ukr. Math. Zh. - 2011. - 63, ¹ 1. - C.102-109.
Serdyuk A.S. Approximation of Poisson integrals by de la Vallée-Poussin sums in uniform and integral metrics // Ukr. Mat. Zh. (2010) 62, No. 12, 1672-1686.
Serdyuk, A.S., Musienko, A.P. The Lebesgue type inequalities for the de la Vallée Poussin sums in approximation of Poisson integrals. (Ukrainian) //
Zb. Pr. Inst. Mat. NAN Ukr.(2010) 7, No. 1, 298-316 .
Serdyuk A.S., Vojtovych, V.A. Approximation of classes of entire functions by interpolation analogues of the de la Vallée Poussin sums. (Ukrainian) // Zb. Pr. Inst. Mat. NAN Ukr.(2010) 7, No. 1, 274-297.
Serdyuk A.S. Approximation of Poisson integrals Valle Poussin sums in uniform and integral metrics // Bulletin of the Slavonic State Pedagogical University.- Mathematics.-1, ¹ 4 .- Slavyansk: SSPU, 2010 .- C.107-127.
A.S. Serdyuk, I.V. Sokolenko, Linear approximation methods and the best approximations of the Poisson integrals of functions from the classes $H_{ω_p} $ in the metrics of the spaces Lp. (Ukrainian; English) Ukr. Mat. Zh. 62, No. 7, 979-996 (2010); translation in Ukr. Math. J. 62, No. 7, 1139-1157 (2010).
Serdyuk A.S., Sokolenko, I.V. The best approximation of Poisson integrals of functions from the class $H_\omega $. Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky, No. 2, 33-37 (2010).
Serdyuk A.S. Approximation of Poisson integrals by Valle'e-Poussinsums in uniform and integral metrics. Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky, No. 6, 34-39 (2009)
Serdyuk A.S., Ovsii E.Yu. Approximation of the classes $C_\beta^\psi H_\omega$ by generalized Zygmund sums. Ukr. Mat. Zh. 61 , No. 4, 524-537 (2009).
Stepanets A.I., Serdyuk, A.S., Shidlich, A.L. Classification of infinitely differentiable periodic functions. Ukr. Mat. Zh. 60, No. 12, 1686-1708 (2008).
Serdyuk A.S. Approximation of Poisson integrals by one linear approximation method in uniform and integral metrics. Ukr. Mat. Zh. 60, No. 7, 976-982 (2008).
Stepanets' O.I., Serdyuk A.S., Shydlich, A.L. On some new criteria of infinite differentiability of periodic functions. Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky, No. 1, 22-26 (2008).
Stepanets' O.I., Serdyuk A.S., Shydlich A.L. On some new criteria of infinite differentiability of periodic functions. Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky, No. 1, 22-26 (2008).
Stepanets' O.I., Serdyuk A.S., Shydlich A.L. On some new criteria for infinite differentiability of periodic functions. Ukr. Mat. Zh. 59, No. 10, 1399-1409 (2007)
Stepanets' O.I., Serdyuk A.S., Shydlich A.L. On some new criteria of infinite differentiability of periodic functions. Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky, No. 1, 22-26 (2008).
Serdyuk A.S. Approximation of classes of analytic functions by Fourier sums in the metric of the space $L_p$. Ukr. Mat. Zh. 57, No. 10, 1395-1408 (2005).
Serdyuk A.S. Approximation of classes of analytic functions by Fourier sums in the uniform metric. Ukr. Mat. Zh. 57, No. 8, 1079-1096 (2005).
Voitsekhivs’kyj, V. R.; Serdyuk, A. S. Jackson type inequalities in approximation of functions from the Sp space by the Voronoi method.(Ukrainian)
Zb. Pr. Inst. Mat. NAN Ukr. 2, No. 2, 43-53 (2005).
Serdyuk A.S. Best approximations and widths of classes of convolutions of periodic functions of high smoothness. Ukr. Mat. Zh. 57, No. 7, 946-971 (2005).
Serdyuk A.S. Approximation of Poisson integrals by de la Vall\'ee Poussin sums. Ukr. Mat. Zh. 56, No. 1, 97-107 (2004).
Serdyuk A.S. Widths in the space Sp of classes of functions defined by the moduli of continuity of their ψ-derivatives. - Extremal Problems in the Theory of Functions and Related Problems: Proceedings of the Institute of Mathematics of NAS of Ukraine. – 2003. – 46. – P. 229–248.
Stepanets A.I. Serdyuk A.S. Direct and indirect theorems of theory of function approximation in the space $S^p$. Ukr. Mat. Zh. 54, No.1,
106-124 (2002).
Serdyuk A.S. Approximation of periodic analytic functions by trigonometric interpolation polynomials in the metric of the space $L$. Ukr. Mat. Zh. 54, No.5, 692-699 (2002).
Serdyuk A.S. Approximation of infinitely differentiable periodic functions by trigonometric interpolation polynomials in integral metric. Ukr. Mat. Zh. 53, No 12, 1654-1663 (2001).
Stepanets A.I., Serdyuk A.S. Approximation of periodic analytic functions by interpolation trigonometric polynomials. Ukr. Mat. Zh. 52, No.12, 1689-1701 (2000).
Stepanets A.I., Serdyuk A.S. Approximation of periodic analytic functions by interpolation trigonometric polynomials. Ukr. Mat. Zh. 52, No.12, 1689-1701 (2000).
Serdyuk A.S. Approximation of periodic functions of high smoothness by interpolation trigonometric polynomials in the metric of $L_1$. Ukr. Mat. Zh. 52, No.7, 994-998 (2000).
Stepanets A.I., Serdyuk A.S. Lebesgue inequalities for Poisson integrals. Ukr. Mat. Zh. 52, No.6, 798-808 (2000).
Stepanets A.I., Serdyuk A.S. Approximations by Fourier sums and best approximations on classes of analytic functions. Ukr. Mat. Zh. 52, No.3, 375-395 (2000).
Stepanets A.I., Serdyuk A.S. Approximations of analytic functions by Fourier sums. Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky, No.12, 20-24 (2000).
Serdyuk A.S. On asymptotically exact error estimates for the approximation of functions of high smoothness by interpolating trigonometric polynomials. Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky, No.8, 29-33 (1999).
Serdyuk A.S. Widths and best approximations for classes of convolutions of periodic functions. Ukr. Mat. Zh. 51, No.5, 674-687 (1999).
Serdyuk A.S. On the existence and uniqueness of a solution of the problem of uniform $SK$-spline interpolation. Ukr. Mat. Zh. 51, No.4, 486-492 (1999).
Stepanets, A.I., Romanyuk, A.S. & Serdyuk, A.S. International conference on the theory of approximation of functions and its applications dedicated to the memory of V. K. Dzyadyk. Ukr Math J 51, 1459–1460 (1999).
doi
Serdyuk A.S. Estimates of the Kolmogorov width of classes of infinitely differentiable periodic functions. Ukr. Mat. Zh. 49, No.12, 1700-1706 (1997).
Serdyuk A.S. On the best approximation of classes of convolutions of periodic functions by trigonometric polynomials. Ukr. Mat. Zh. 47, No.9, 1261-1265 (1995).
Stepanets A.I., Serdyuk A.S. Lower bounds for widths classes of convolutions of periodic functions in $C$ and $L$ metric. Ukr. Mat. Zh. 47, No.8, 1112-1121 (1995).
Stepanets A.I., Serdyuk A.S. On the existence of interpolating $SK$-splines. Ukr. Mat. Zh. 46, No.11, 1546-1553 (1994).