On the best mean-square approximation by entire functions of finite type on the line

S.B. Vakarchuk (Dnipropetrovsk University of Economics and Law), https://orcid.org/0000-0002-2562-8844
M.B. Vakarchuk (Oles Honchar Dnipropetrovsk National University), https://orcid.org/0000-0001-8606-9057

Abstract


Jackson-type inequalities have been obtained for the best mean square approximation of differentiable functions by means of the entire functions of finite type on the line.

References


Vakarchuk S.B. "Jackson-type inequalities and widths of function classes in $$$L_2$$$", Math. Notes, 2006; 80(1): pp. 11-18. doi:10.1007/s11006-006-0102-y

Vakarchuk S.B., Shchitov A.N. "The best polynomial approximations in $$$L_2$$$ and widths of some classes of functions", Ukrainian Math. J., 2004; 56(11): pp. 1458-1466. (in Russian) doi:10.1007/s11253-005-0148-0

Ibragimov I.I., Nasibov F.G. "On the estimation of the best approximation of summable function on the real domain by entire functions of finite degree", Dokl. AN SSSR, 1970; 194(5): pp. 1013-1016. (in Russian)

Nasibov F.G. "On approximation in $$$L_2$$$ by entire functions", Dokl. AN Azerb. SSR, 1986; 42(4): pp. 3-6. (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)

Taikov L.V. "Inequalities containing the best approximations and the modulus of continuity of functions in $$$L_2$$$", Matem. zametki, 1976; 20(3): pp. 433-438. (in Russian) doi:10.1007/BF01097254

Shalaev V.V. "On widths in $$$L_2$$$ of classes of differentiable functions, defined by moduli of continuity of the highest orders", Ukrainian Math. J., 1991; 43(1): pp. 125-129. (in Russian) doi:10.1007/BF01066914

Vakarchuk S.B. "Exact constant in an inequality of Jackson type for $$$L_2$$$-approximation on the line and exact values of mean widths of functional classes", East J. Approx., 2004; 10(1-2): pp. 27-39.




DOI: https://doi.org/10.15421/240906

  

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Copyright (c) 2009 S.B. Vakarchuk, M.B. Vakarchuk

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