Jackson type inequalities for moduli of continuity of arbitrary order are established with the use of linear approximation methods. The constants are smaller than known previously. The results hold in different spaces of periodic and nonperiodic functions. Bibliography: 19 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 383, 2010, pp. 33–52. Original
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Vinogradov, O.L., Zhuk, V.V. The rate of decrease of constants in Jackson type inequalities in dependence of the order of the continuity modulus. J Math Sci 178, 132–143 (2011). https://doi.org/10.1007/s10958-011-0532-2
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DOI: https://doi.org/10.1007/s10958-011-0532-2