Modulus of smoothness: Difference between revisions

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===Moduli of smoothness===

The generalization of the conception of the [[modulus of continuity]] is the modulus of smoothness. If for a contionuous function <math>f</math> the modulus of contuniuty is enough small, then the function is constant. Therefore forFor higher smoothness we can't use such a criterior as a modulus of continuity. SomeThe propertiesmeasure of smoothness of a function can be described in terms of a modulus of smoothness. It is used as a good tool for the elegant estimation of the rate of the approximation function by [[Bernstein polynomial]].

In some problems in the approximation theory, as the characterization of the best algebraic approximation, the moduli of smoothness are widely used.

Modulus of smoothness of order n