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A convergent quasi-Hermite-Féjer interpolation process

Published online by Cambridge University Press:  17 April 2009

T.M. Mills
T.M. Mills
Affiliation:
Department of Mathematics, Eastern Montana College, Billings, Montana, USA.
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Abstract

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D.L. Berman has proved several divergence theorems about “extended” Hermite-Fejér interpolation on the Chebyshev nodes of the first kind. These are surprising in light of the classical convergence theorem of L. Fejér concerning ordinary Hermite-Fejér interpolation on these nodes. However there is one case which has been neglected so far: the case of quasi-Hermite-Fejér interpolation on these nodes. In this paper it is proved that quasi-Hermite-Fejér interpolation polynomials on the Chebyshev nodes converge uniformly to the continuous function being interpolated. In addition, an estimate for the rate of convergence is established.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 2 , April 1975 , pp. 267 - 276
Copyright
Copyright © Australian Mathematical Society 1975

References

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