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A property of Bernstein-Schoenberg spline operators

Published online by Cambridge University Press:  20 January 2009

T. N. T. Goodman  and
A. Sharma
T. N. T. Goodman
Affiliation:
Department of Mathematical Sciences, University of Dundee, Dundee DD1 4HN, Scotland, U.K.
A. Sharma
Affiliation:
Department of Mathematical Sciences, University of Dundee, Dundee DD1 4HN, Scotland, U.K.
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Let Bnf; x) denote the Bernstein polynomial of degree n on [0,1] for a function f(x) defined on this interval. Among the many properties of Bernstein polynomials, we recall in particular that if f(x) is convex in [0,1] then (i) Bn(f;x) is convex in [0,1] and (ii) Bn(f;x)≧Bn+1(f;x), (n = l,2,…). Recently these properties have been the subject of study for Bernstein polynomials over triangles [1].

Type
Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 28 , Issue 3 , October 1985 , pp. 333 - 340
Copyright
Copyright © Edinburgh Mathematical Society 1985

References

REFERENCES

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