We propose a new method for proving Jackson type inequalities for not necessarily periodic functions defined on the whole real line. In the inequalities under consideration, the best approximations by entire functions of exponential type are estimated in terms of the moduli of continuity of the derivatives of the approximated function. For some values of the parameters the obtained constants are less than the known ones. We construct linear approximation methods for realizing the obtained inequalities.
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Translated from Problemy Matematicheskogo Analiza 114, 2022, pp. 3-13.
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Babushkin, M.V., Vinogradov, O.L. On Constants in Estimates of Approximations by Entire Functions of Exponential Type in Terms of Moduli of Continuity of Derivatives. J Math Sci 261, 353–365 (2022). https://doi.org/10.1007/s10958-022-05755-6
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DOI: https://doi.org/10.1007/s10958-022-05755-6