### Inequalities of Jackson-Stechkin type for $$$B^2$$$-almost periodic functions

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Chernykh N.I. "On Jackson inequality in $$$L_2$$$", *Trudy MIAN SSSR*, 1967; 88: pp. 71-74. (in Russian)

Chernykh N.I. "On the best approximation of periodic functions by trigonometrical polynomials in $$$L_2$$$", *Matem. zametki*, 1967; 2(5): pp. 513-522. (in Russian)

Vasil'ev S.N. "Jackson-Stechkin inequality in $$$L_2[-\pi;\pi]$$$", *Trudy in-ta matem. i mekhan. UrO RAN*, 2001; 7(1): pp. 75-84. (in Russian)

Stepanets A.I., Serduk A.S. "Direct and inverse theorems of functions approximation theory in $$$S^p$$$ space", *Ukrainian Math. J.*, 2002; 54(1): pp. 106-124. (in Russian)

Vasil'ev S.N. "Sharp Jackson-Stechkin inequality in $$$L_2$$$ with the modulus of continuity, generated by arbitrary finite-difference operator with constant coefficients", *Dokl. RAN*, 2002; 385(1): pp. 11-14. (in Russian)

Shapiro H.S. "Tauberian theorem related to approximation theory", *Acta Math.*, 1968; 120: pp. 279-292.

Shapiro H.S., Boman J. "Comparison theorems for a generalized modulus of continuity", *Arkiv for Matematik*, 1971; 9(1): pp. 91-116.

Boman J. "Equivalence of generalized moduli of continuity", *Arkiv for Matematik*, 1980; 18(1): pp. 73-100.

Babenko A.G. "On exact constant in Jackson inequality", *Matem. zametki*, 1986; 39(5): pp. 651-664. (in Russian)

Kozko A.I., Rozhdestvenskij A.V. "On Jackson inequality with generalized modulus of continuity", *Matem. zametki*, 2003; 73(5): pp. 783-788. (in Russian)

Kozko A.I., Rozhdestvenskij A.V. "On Jackson inequality with generalized modulus of continuity", *Matem. sbornik*, 2004; 195(8): pp. 3-46. (in Russian)

Pritula Ya.G. "On Jackson inequality for $$$B^2$$$-almost periodic functions", *Izvestiya VUZov. Matematika*, 1972; 123(8): pp. 90-93. (in Russian)

Babenko V.F., Savela S.V. "Inequalities of Jackson-Stechkin type for $$$B^2$$$-almost periodic functions", *Dnipr. Univ. Math. Bull.*, 2011; 19(6/1): pp. 8-14. (in Russian)

Levitan B.M. *Almost periodic functions*, Moscow, 1953; 396 p. (in Russian)

Bredikhina Ye.A. "Almost periodic functions", *Mathematical Encyclopedia*, Moscow, 1984; 4: pp. 543-545. (in Russian)

Bredikhina Ye.A. "On absolute convergence of Fourier series of almost periodic functions", *Dokl. AN SSSR*, 1968; 179(6): pp. 1023-1026. (in Russian)

DOI: https://dx.doi.org/10.15421/241208

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