### Behaviour of exact constants in inequalities of Jackson type

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Korneichuk N.P. "Exact constant in Jackson theorem of the best uniform appproximation of continuous periodic functions", *Dokl. AN SSSR*, 1962; 145: pp. 514-515. (in Russian)

Korneichuk N.P. *Extremum problems in approximation theory*, Moscow, 1976; 320 p. (in Russian)

Korneichuk N.P. *Exact constants in approximation theory*, Nauka, Moscow, 1987; 424 p. (in Russian)

Timan A.F. *Approximation theory for real-variable functions*, Fizmatgiz, Moscow, 1960; 624 p. (in Russian)

Chernykh N.I. "On Jackson inequality in $$$L_2$$$ space", *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) doi:10.1007/BF01093942

Gavriliuk V.T. "Approximation of continuous periodic functions by Rogozinskii sums and Fourier sums", *Problems of func. approx. theory and its appl.*, Kyiv, 1976; pp. 46-60. (in Russian)

Korneichuk N.P., Ligun A.A., Doronin V.G. *Approximation with constraints*, Kyiv, 1982; 250 p. (in Ukrainian)

Babenko V.F. "Non-symmetric approximations in spaces of integrable functions", *Ukrainian Math. J.*, 1982; 34(4); pp. 409-416. (in Russian) doi:10.1007/BF01091584

Babenko V.F. "Non-symmetric extremum problems of approximation theory", *Dokl. AN SSSR*, 1983; 269(3): pp. 521-524. (in Russian)

Ligun A.A. *Special problems of approximation theory*, Kyiv, 1990. (in Russian)

Doronin V.G. "On the order of grow of exact constants in inequalities of Jackson type for the best one-sided approximations", *Proc. Int. Conf.: Kaluga: Approx. Theory*, 1996; pp. 90-91. (in Russian)

Ligun A.A. "Jackson's type inequalities", *East J. Approx.*, 1996; 2(2): pp. 235-244.

Doronin V.G. "On the order of grow of exact constants in inequalities of Jackson type for the best $$$(\alpha, \beta)$$$-approximations", *Proc. II Int. School: Fourier series*, Kyiv, 1997; pp. 47-48. (in Ukrainian)

Babenko A.G. *Direct theorems of approximation theory in $$$L_2$$$ and associated extremal problems for positive defined functions: Diss. for doct.phys.-math.sc.*, Ekaterinburg, 2004. (in Russian)

DOI: https://doi.org/10.15421/240810

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