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On the Hölder semi-norm of the remainder in polynomial approximation

Published online by Cambridge University Press:  17 April 2009

David Elliott
David Elliott
Affiliation:
Department of MathematicsUniversity of TasmaniaGPO Box 252C Hobart Tas 7001Australia
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Suppose the qth derivative of a function f is Hölder continuous of index α, where 0 < α ≤ 1, on the interval [-1,1]. Suppose further that pn is any polynomial of degree at most n such that |τn(x)| = |f(x) - pn(x)| ≤ c {max ((1 - x2)½/n, 1/n2) } q+a [-1,1]. If

then it is shown that

‖τn‖β ≤ cn−q−α+β, 0 < β ≤ 1.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 3 , June 1994 , pp. 421 - 426
Copyright
Copyright © Australian Mathematical Society 1994

References

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