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On approximation in spaces of continuous functions

Published online by Cambridge University Press:  17 April 2009

Heinz H. Gonska
Heinz H. Gonska
Affiliation:
University of Duisburg, Department of Mathematics, D-4100 Duisburg I, West Germany; Department of Mathematical Sciences, Drexel University, Philadelphia, Pennsylvania 19104, USA.
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Abstract

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This paper deals with approximation of certain operators defined on the space C(X) of real-valued continuous functions on an arbitrary compact metric space (X, d). In particular the problem of giving quantitative Korovkin type theorems for approximation by positive linear operators is solved. This is achieved by using a smoothing approach and the least concave majorant of the modulus of continuity of a function f in C(X). Several new estimates are given as applications, including such for Shepard's method of metric interpolation.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 28 , Issue 3 , December 1983 , pp. 411 - 432
Copyright
Copyright © Australian Mathematical Society 1983

References

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