Abstract
We establish lower and upper bounds for the quantity
, where
, and D m (t) is the Dirichlet kernel, for the class W r of 2π-periodic functions, whose rth derivative satisfies the condition |f r(x)| ≤ 1.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 12, pp. 1691 – 1698, December, 2004.
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Grigoryan, A.L. Estimate of the Remainder of the Best Quadratic Approximation of Differentiable Functions by Polynomials. Ukr Math J 56, 1998–2006 (2004). https://doi.org/10.1007/s11253-005-0164-0
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DOI: https://doi.org/10.1007/s11253-005-0164-0