Mathematical Notes

, Volume 93, Issue 5–6, pp 917–922 | Cite as

Sharp constant in Jackson’s inequality with modulus of smoothness for uniform approximations of periodic functions

  • S. A. PichugovEmail author


It is proved that, in the space C, 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.


Jackson’s inequality periodic function trigonometric polynomial modulus of smoothness polygonal line Steklov mean Favard sum 


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© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Dnepropetrovsk National Technical University of Railroad CommunicationsKievRussia

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