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Improvement of Jackson Type Inequalities for Moduli of Continuity of Order 4, 6, 8

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We prove estimates for the best approximations by entire functions of exponential type in terms of the moduli of continuity of order 4, 6, and 8. The constants in the obtained estimates are less than the known constants in such estimates for some values of step. All the obtained estimates are realized by linear approximation methods. Bibliography: 7 titles.

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References

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

    O. L. Vinogradov

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  1. O. L. Vinogradov
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Correspondence to O. L. Vinogradov.

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Translated from Problemy Matematicheskogo Analiza 82, September 2015, pp. 59-70.

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Vinogradov, O.L. Improvement of Jackson Type Inequalities for Moduli of Continuity of Order 4, 6, 8. J Math Sci 210, 622–634 (2015). https://doi.org/10.1007/s10958-015-2581-4

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  • DOI: https://doi.org/10.1007/s10958-015-2581-4

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