Abstract
It is proved that, in the space C2π, for all k, n ∈ ℕ,n > 1, the following inequalities hold:
where e n−1(f) is the value of the best approximation of f by trigonometric polynomials and ω 2(f, h) is the modulus of smoothness of f. A similar result is also obtained for approximation by continuous polygonal lines with equidistant nodes.
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Original Russian Text © S. A. Pichugov, 2013, published in Matematicheskie Zametki, 2013, Vol. 93, No. 6, pp. 932–938.
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Pichugov, S.A. Sharp constant in Jackson’s inequality with modulus of smoothness for uniform approximations of periodic functions. Math Notes 93, 917–922 (2013). https://doi.org/10.1134/S0001434613050295
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DOI: https://doi.org/10.1134/S0001434613050295