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Splicing n-Convex Functions using Splines

Published online by Cambridge University Press:  20 November 2018

G. E. Cross
G. E. Cross*
Affiliation:
Department of Pure Mathematics University of Waterloo, Waterloo, Ontario N2L3G1
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Abstract

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It is proved that a regular piecewise n-convex function differs from an n-convex function only by a polynomial spline of degree n - 1. The argument is given in terms of Peano and de la Vallée Poussin derivatives.

Keywords

26A5141A15n-convex functionSplines
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 1 , 01 March 1980 , pp. 107 - 109
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Bullen, P. S., A Criterion For n-Convexity, Pacific J. Math. vol. 36 (1971) pp. 81-98.Google Scholar
2. Cross, G. E., The Pn-integral, Canad. Math. Bull. vol. 18 (1975) pp. 493-497.Google Scholar
3. James, R. D., Generalized nth primitives, Trans. Amer. Math. Soc. vol. 76 (1954) pp. 149-176.Google Scholar
4. Prenter, P. M., Splines and Variational Methods, John Wiley, 1975.Google Scholar