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On Jackson Type Inequalities for the Best Approximations of Periodic Functions

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We develop a new approach to the proof of a generalized Jackson theorem providing an estimate for the best approximation by trigonometric polynomials with the help of the moduli of continuity of an arbitrary order. The proposed approach is based on approximation methods constructed by using Fejer and Jackson–Vallee - Poussin classical kernels. Bibliography: 14 titles.

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  1. St. Petersburg State University, 28, Universitetskii pr., St. Petersburg, 198504, Russia

    V. V. Zhuk

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  1. V. V. Zhuk
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Correspondence to V. V. Zhuk.

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Translated from Problemy Matematicheskogo Analiza 82, September 2015, pp. 89-98.

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Zhuk, V.V. On Jackson Type Inequalities for the Best Approximations of Periodic Functions. J Math Sci 210, 654–663 (2015). https://doi.org/10.1007/s10958-015-2584-1

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