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Error bounds in the approximation of functions

Published online by Cambridge University Press:  17 April 2009

Badri N. Sahney  and
V. Venu Gopal Rao
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
Information
Bulletin of the Australian Mathematical Society , Volume 6 , Issue 1 , February 1972 , pp. 11 - 18
Copyright
Copyright © Australian Mathematical Society 1972

References

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