Modulus of smoothness: Difference between revisions

Revision as of 16:17, 20 December 2014

Revision as of 17:20, 20 December 2014

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The generalization of the conception of the [[modulus of continuity]] is the modulus of smoothness. If for contionuous function the modulus of contuniuty is enough small, then the function is constant. For higher smoothness we can't use such a criterior as a modulus of continuity. The measure 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]].

InThere are some problems in the approximation theory, as the characterization of the best algebraic approximation, for which the moduli of smoothness are widelycommonly used.

Modulus of smoothness of order n