Modulus of smoothness: Difference between revisions

Revision as of 10:19, 5 December 2014

Revision as of 10:21, 5 December 2014

Line 2:

<!-- EDIT BELOW THIS LINE -->

===Moduli of smoothness===

Modulus of smoothness of order n of a function f∈C[a,b] is the function <math>\omega_n</math>:[0,∞\infty)→ℝ\rightarrow\mathbb{R}</math> defined by

<math>\omega_n(t,f,[a,b])=\sup_{h\in[0,t]}\sup_{x\in[a,b-nh]}|\Delta_h^n(f,x)|,</math>

for <math>t\in[0,\frac{b-a}{n}],</math> and