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New Telyakovskii-type estimates via the Boolean sum approach

Published online by Cambridge University Press:  17 April 2009

Jia-Ding Cao  and
Heinz H. Gonska
Jia-Ding Cao
Affiliation:
Department of Mathematics, Fudan University, Shanghai 200 433, People's Republic of China
Heinz H. Gonska
Affiliation:
Department of Mathematics, University of Duisburg, D-47048 Duisburg, Germany
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Abstract

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In the present note the magnitude of constants in Telyakovskii-type theorems is investigated. Our general approach to construct the linear operators yielding good constants is the one via Boolean sums. Explicit values for the constants in question are given for general convolution-type operators; the classical Fejér-Korovkin kernel is then used as an example for which one obtains rather small values. Furthermore, also an asymptotic assertion is derived which indicates the room left for improvement of the main results. This leads to a natural conjecture concluding this article.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 1 , August 1996 , pp. 131 - 146
Copyright
Copyright © Australian Mathematical Society 1996

References

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