### On the best polynomial approximation of $$$2\pi$$$-periodic functions in the $$$L_2$$$ space

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Ditzian Z., Totik V. *Moduli of Smoothness*, Springer-Verlag, New York, 1987; 227 p. doi:10.1007/978-1-4612-4778-4

Sendov B., Popov V. *Averaged moduli of smoothness*, Mir, Moscow, 1988; 328 p. (in Russian)

Trigub R.M. "Absolute convergence of Fourier integrals, summability of Fourier series, and polynomial approximation of functions on a torus", *Izv. AN SSSR. Ser. mat.*, 1980; 44(6): pp. 1378-1409. (in Russian) doi:10.1070/IM1981v017n03ABEH001372

Runovskij K.V. "On approximation by set of linear polynomial operators in $$$L_p$$$ space, $$$0 < p < 1$$$", *Mat. sb.*, 1994; 185(8): pp. 81-102. (in Russian)

Pustovojtov N.P. "Estimation of the best approximations of periodic functions with trigonometric polynomials by average differences and multidimensional Jackson theorem", *Mat. sb.*, 1997; 188(10): pp. 95-109. (in Russian) doi:10.1070/SM1997v188n10ABEH000265

Vakarchuk S.B. "On the best polynomial approximations in $$$L_2$$$ of some classes of $$$2\pi$$$-periodic functions and exact values of their $$$n$$$-widths", *Matem. zametki*, 2001; 70(3): pp. 334-345. (in Russian) doi:10.1023/A:1012335526330

Vakarchuk S.B., Zabutnaya V.I. "Some problems in theory of approximation of classes of $$$2\pi$$$-periodic functions in $$$L_p$$$ spaces, $$$1 \leqslant p \leqslant \infty$$$", *Zb. pr. In-tu matematyky NAN Ukrajiny (Problems of functions approximation theory and adjacent problems)*, Kyiv, 2004; 1(1): pp. 25-41. (in Russian)

Vakarchuk S.B., Zabutnaya V.I. "Inequalities of Jackson-Stechkin type for special moduli of continuity and widths of functional classes in $$$L_2$$$", *Mat. zametki*, 2012; 92(4): pp. 497-514. (in Russian)

Shabozov M.Sh., Vakarchuk S.B., Zabutnaya V.I. "Sharp inequalities of Jackson-Stechkin type for periodic functions in $$$L_2$$$ and values of widths of functional classes", *Dokl. RAN*, 2013; 451(6): pp. 625-628. (in Russian) doi:10.1134/S106456241304039X

Pinkus A. *n-Widths in approximation theory*, Springer-Verlag, Berlin, 1985; 290 p.

DOI: https://doi.org/10.15421/241503

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