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Approximation of Continuous Functions by de La Vallee-Poussin Operators

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Abstract

We study the asymptotic (as σ → ∞) behavior of upper bounds of the deviations of functions belonging to the classes \(\hat C_\infty ^{\bar \psi }\) and \(\hat C^{\bar \psi } H_\omega\) from the so-called de la Vallee-Poussin operators. We obtain asymptotic equalities that, in some important cases, give a solution of the Kolmogorov-Nikol’skii problem for the de la Vallee-Poussin operators on the classes \(\hat C_\infty ^{\bar \psi }\) and \(\hat C^{\bar \psi } H_\omega\).

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  1. Slavyansk Pedagogic University, Slavyansk, Ukraine

    V. I. Rukasov & E. S. Silin

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  1. V. I. Rukasov
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  2. E. S. Silin
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 2, pp. 230–238, February, 2005.

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Rukasov, V.I., Silin, E.S. Approximation of Continuous Functions by de La Vallee-Poussin Operators. Ukr Math J 57, 271–281 (2005). https://doi.org/10.1007/s11253-005-0187-6

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  • DOI: https://doi.org/10.1007/s11253-005-0187-6

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