Some modifications of Jackson-type inequalities are established, including estimates on the best approximations of periodic functions by trigonometric polynomials in terms of the moduli of continuity of higher orders. Special attention is paid to bounding the constants occurring in the inequalities obtained.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 418, 2013, pp. 28–59.
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Babushkin, M.V., Zhuk, V.V. On the Constants in Generalized Jackson-Type Inequalities. J Math Sci 200, 532–550 (2014). https://doi.org/10.1007/s10958-014-1942-8
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DOI: https://doi.org/10.1007/s10958-014-1942-8