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On the relative behaviour of moduli of smoothness

Published online by Cambridge University Press:  17 April 2009

S.P. Zhou
S.P. Zhou
Affiliation:
Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax NS, CanadaB3H 3J5
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Abstract

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Some general theorems concerning the relative behaviour of moduli of smoothness are established. In particular an open problem raised by Dickmeis, Nessel and van Wickeren is negated.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 3 , June 1991 , pp. 475 - 482
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Marchaud, A., ‘Sur les dérivées et sur les différences des fonctions de variables réelles’, J. Math. Pures Appl. 6 (1927), 337–425.Google Scholar
[2]Dickmeis, W., Nessel, R.J. and van Wickeren, E., ‘Problem No.5: Relative behavior of moduli of continuity’, in Second Edmonton Conference on Approximation Theory, pp. 391–392 (Amer. Math. Soc., Providence, Rhode Island, 1983).Google Scholar