Behaviour of exact constants in inequalities of Jackson type

V.G. Doronin (Oles Honchar Dnipropetrovsk National University)
A.A. Ligun (Oles Honchar Dnipropetrovsk National University)

Abstract


We studied the behaviour of exact constants in inequalities of Jackson type in $$$L_p$$$ space.

References


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)


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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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