References
- Belov A.S. Remarks on Mean Convergence (Boundedness) of Partial
Sums of Trigonometric Series. Math. Notes 2002, 71
(5-6), 739–748. doi:10.1023/A:1015860510199 (translation of Mat. Zametki
2002, 71 (6) 807–817. doi:10.4213/mzm386 (in
Russian))
- Bushev D.M. Approximation of classes of continuous periodic functions
by Zygmund sums. Preprint. Inst. Math. AN USSR, Kyiv, 1984. (in
Russian)
- Dzyadyk V.K. On best approximation in classes of periodic
functions defined by integrals of a linear combination of absolutely
monotonic kernels. Math. Notes 1974, 16 (5),
1008–1014. doi:10.1007/BF01149788 (translation of Mat. Zametki 1974,
16 (5), 691–701. (in Russian))
- Hrabova U.Z., Serdyuk A.S. Order estimates for the best
approximations and approximations by Fourier sums of the classes of
\((\psi,\beta)\)-differential
functions. Ukrainian Math. J. 2014, 65 (9),
1319–1331. doi:10.1007/s11253-014-0861-7 (translation of Ukrain. Mat.
Zh. 2013, 65 (9), 1186–1197. (in Ukrainian))
- Kamzolov A.I. Approximation of the functional classes \(\widetilde{W}^{\alpha}_{p}(L)\) in the
spaces \(\mathcal L_{p}[-\pi,\pi]\) by
the Fejér method. Math. Notes 1978, 23 (3),
185–189. doi:10.1007/BF01651429 (translation of Mat. Zametki 1978,
23 (3), 343–349. (in Russian))
- Kostich M. V. Approximation of functions from Weyl-Nagy classes
by Zygmund averages. Ukrainian Math. J. 1998, 50
(5), 834–838. doi:10.1007/BF02514336 (translation of Ukrain. Mat. Zh.
1998 50 (5), 735–738. (in Ukrainian))
- Nagy B.Sz. Sur une classe générale de procèdès de sommation pour
les sèries de Fourier. Acta Math. Hungar. 1948, 1
(3), 14–52.
- Nikolskii S.M. Approximation of periodic functions by
trigonometric polynomials. Tr. Mat. Inst. Steklova 1945,
15, 3–76. (in Russian)
- Pinkus A. \(n\)-Widths in
approximation theory. Springer-Verlag, Berlin, 1985.
doi:10.1007/978-3-642-69894-1
- Serdyuk A.S. On the best approximation of classes of convolutions
of periodic functions by trigonometric polynomials. Ukrainian Math.
J. 1995, 47 (9), 1435–1440. doi:10.1007/BF01057518
(translation of Ukrain. Mat. Zh. 1995, 47 (9),
1261–1265. (in Russian))
- Serdyuk A.S. Widths and best approximations for classes of
convolutions of periodic functions. Ukrainian Math. J. 1999,
51 (5), 748–763. doi:10.1007/BF02591709 (translation of
Ukrain. Mat. Zh. 1999, 51 (5), 674–687. (in
Ukrainian))
- Serdyuk A.S. On best approximation in classes of convolutions of
periodic functions. Approx. Theory of Functions and Related
Problems. Proc. Inst. Math. NAS Ukr. 2002, 35, 172–194.
(in Ukrainian)
- Serdyuk A.S. Best approximations and widths of classes of
convolutions of periodic functions of high smoothness. Ukrainian
Math. J. 2005, 57 (7), 1120–1148.
doi:10.1007/s11253-005-0251-2 (translation of Ukrain. Mat. Zh. 2005,
57 (7), 946–971. (in Ukrainian))
- Serdyuk A.S., Hrabova U.Z. Estimates of uniform approximations by
Zygmund sums on classes of convolutions of periodic functions.
Approx. Theory of Functions and Related Problems. Proc. Inst. Math. NAS
Ukr. 2013, 10 (1), 222–244. (in Ukrainian)
- Serdyuk A. S., Sokolenko I. V. Uniform approximation of the
classes of \((\psi,\beta)\)-differentiable functions by
linear methods. Extremal Problems of the Theory of Functions and
Related Problems. Proc. Inst. Math. NAS Ukr. 2011, 8
(1), 181–189. (in Ukrainian)
- Serdyuk A.S., Sokolenko I. V. Asymptotic estimates for the best
uniform approximations of classes of convolution of periodic functions
of high smoothness. Ukr. Mat. Visn. 2020, 17 (3),
396–413. (in Ukrainian)
- Serdyuk A.S., Stepanyuk T.A. Estimations of the best
approximations for the classes of infinitely differentiable functions in
uniform and integral metrics. Ukrainian Math. J. 2014,
66 (9), 1393–1407. doi:10.1007/s11253-015-1018-z
(translation of Ukrain. Mat. Zh. 2014, 66 (9),
1244–1256. (in Ukrainian))
- Serdyuk A.S., Stepanyuk T.A. Order estimates for the best
approximations and approximations by Fourier sums in the classes of
convolutions of periodic functions of low smoothness in the uniform
metric. Ukrainian Math. J. 2014, 66 (12),
1862–1882. doi:10.1007/s11253-015-1056-6 (translation of Ukrain. Mat.
Zh. 2014, 66 (12), 1658–1675. (in Ukrainian))
- Serdyuk A.S., Stepanyuk T.A. Uniform approximations by Fourier
sums in classes of generalized Poisson integrals. Anal. Math. 2019,
45 (1), 201–236. doi:10.1007/s10476-018-0310-1
- Stepanets A.I. Methods of Approximation Theory. Walter de Gruyter,
Berlin, 2005.
- Stepanyuk T.A. Estimates for the best approximations and
approximation by Fourier sums of classes of convolutions of periodic
functions of not high smoothness in integral metrics. Approx.
Theory of Functions and Related Problems. Proc. Inst. Math. NAS Ukr.
2014, 11 (3), 241–269. (in Ukrainian)
- Sz.-Nagy B. Über gewisse Extremalfragen bei transformierten
trigonometrischen Entwicklungen. Berichte der math.-phys. Kl. Akad.
der Wiss. zu Leipzig, 1938, 90, 103–134.
- Telyakovskii S. A. On the norms of trigonometric polynomials and
approximation of differentiable functions by linear averages of their
Fourier series. Tr. Mat. Inst. Steklova 1961, 62,
61–97. (in Russian)
- Temlyakov V.N. Approximation of periodic functions. Computational
Mathematics and Analysis Series. Nova Science Publ. Inc., NY, 1993.
- Tikhomirov V.M. Some questions in approximation theory. Moscow Univ.
Publ., Moscow, 1976. (in Russian)
- Tikhonov S. Trigonometric series with general monotone
coefficients. J. Math. Anal. Appl. 2007, 326 (1),
721–735. doi:10.1016/j.jmaa.2006.02.053
- Zygmund A. Smooth functions. Duke Math. J. 1945,
12 (1), 47–76. doi:10.1215/S0012-7094-45-01206-3
- Zygmund A. Trigonometric series. Vol. 2. Mir, Moscow, 1965. (in
Russian)