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Error bounds in the approximation of functions

Published online by Cambridge University Press:  17 April 2009

Badri N. Sahney
Affiliation:
Department of Mathematics, Statistics and Computer Science, The University, Calgary, Alberta, Canada;
V. Venu Gopal Rao
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
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Let f(x) ε Lipα, 0 < α < 1, in the range (-π, π), and periodic with period 2π, outside this range. Also let

.

We define the norm as

and let the degree of approximation be given by

where Tn (x) is some n–th trigonometric polynomial.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1972

References

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