Abstract
We study some problems of the approximation of continuous functions defined on the real axis. As approximating aggregates, the de la Vallee-Poussin operators are used. We establish asymptotic equalities for upper bounds of the deviations of the de la Vallee-Poussin operators from functions of low smoothness belonging to the classes \(\hat C^{\bar \psi } \mathfrak{N}\).
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REFERENCES
A. I. Stepanets, Wang Kunyang, and Zhang Xirong, “Approximation of locally integrable function on the real line,” Ukr. Mat. Zh., 51, No.11, 1549–1561 (1999).
A. I. Stepanets, “Classes of functions defined on the real axis and their approximation by entire functions. I,” Ukr. Mat. Zh., 42, No.1, 102–112 (1990).
A. I. Stepanets, “Classes of functions defined on the real axis and their approximation by entire functions. II,” Ukr. Mat. Zh., 42, No.2, 210–222 (1990).
A. I. Stepanets, “Approximation of functions defined on the real axis by Fourier operators,” Ukr. Mat. Zh., 40, No.2, 198–209 (1988).
A. I. Stepanets, “Approximation in spaces of locally integrable functions,” Ukr. Mat. Zh., 46, No.5, 597–625 (1994).
V. I. Rukasov, “Approximation of functions defined on the real axis by de la Vallee-Poussin operators,” Ukr. Mat. Zh., 44, No.5, 682–691 (1992).
V. I. Rukasov, “Approximation of continuous functions by de la Vallee-Poussin operators,” Ukr. Mat. Zh., 55, No.3, 414–424 (2003).
A. I. Stepanets, Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987).
A. I. Stepanets, “Approximation of \({\bar \psi }\)-integrals of periodic functions by Fourier sums (low smoothness). II,” Ukr. Mat. Zh., 50, No.3, 388–400 (1998).
V. I. Rukasov, O. A. Novikov, and S. O. Chaichenko, “Approximation of classes of periodic functions with low smoothness by de la Vallee-Poussin sums,” in: Theory of Approximation of Functions and Related Problems [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv (2002), pp. 119–133.
V. I. Rukasov and S. O. Chaichenko, “Approximation of continuous periodic functions by de la Vallee-Poisson sums (low smoothness),” in: Theory of Approximation of Functions and Related Problems [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv (2002), pp. 134–150.
A. I. Stepanets, Methods of Approximation Theory [in Russian], Vol. 1, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (2002).
V. I. Rukasov and S. O. Chaichenko, “Approximation of the classes C ψ H ω by de la Vallee-Poussin sums,” Ukr. Mat. Zh., 54, No.5, 681–691 (2002).
V. I. Rukasov and E. S. Silin, “Approximation of continuous functions by de la Vallee-Poussin operators,” in: Extremal Problems in the Theory of Functions and Related Problems [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv (2003), pp. 192–208.
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 3, pp. 394–399, March, 2005.
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Rukasov, V.I., Silin, E.S. Approximation of Continuous Functions of Low Smoothness by de la Vallee-Poussin Operators. Ukr Math J 57, 474–480 (2005). https://doi.org/10.1007/s11253-005-0204-9
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DOI: https://doi.org/10.1007/s11253-005-0204-9