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For example, moduli of smoothness are used in Whitney inequality to estimate the error of local polynomial approximation. Another application is given by the more general version of Jackson inequality.
We can also state a more general version of [[https://en.wikipedia.org/wiki/Jackson's_inequality| Jackson inequality]]:
For every natural number n, there exists a constant W(k) such that for any continuous function f on <math>[a,b]</math> we have
<math>E_{n-1}(f)_{[a,b]}\leq W(k)\omega_k\left(\frac{b-a}{k},f,[a,b]\right).</math>
== Mathematical analysis / Moduli of smoothness ==
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