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

V.F. Babenko (Oles Honchar Dnipropetrovsk National University), https://orcid.org/0000-0001-6677-1914
S.V. Savela (Oles Honchar Dnipropetrovsk National University)

Abstract


We obtain the exact inequalities of Jackson-Stechkin type for approximation of $$$B^2$$$-almost periodic functions.

Keywords


best approximation; $$$B^2$$$-almost periodic function; inequalities of the Jackson type

References


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

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

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

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

Popov V.Yu. "On the best mean-square approximations by entire functions of exponential type", Izv. vuzov. Matem., 1972; 121(6): pp. 65-73. (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)

Chernykh N.I. "On Jackson inequalities 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




DOI: https://doi.org/10.15421/241102

  

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Copyright (c) 2011 V.F. Babenko, S.V. Savela

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