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A generalization of the Bernstein polynomials

Published online by Cambridge University Press:  20 January 2009

Haul Oruç ,
George M. Phillips  and
Philip J. Davis
Haul Oruç
Affiliation:
Mathematical Institute, University of St Andrews, North Haugh St Andrews, Fife KY16 9SS, Scotland
George M. Phillips
Affiliation:
Mathematical Institute, University of St Andrews, North Haugh St Andrews, Fife KY16 9SS, Scotland
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This paper is concerned with a generalization of the classical Bernstein polynomials where the function is evaluated at intervals which are in geometric progression. It is shown that, when the function is convex, the generalized Bernstein polynomials Bn are monotonic in n, as in the classical case.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 2 , June 1999 , pp. 403 - 413
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

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