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Splicing n-Convex Functions using Splines

Published online by Cambridge University Press:  20 November 2018

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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1980

References

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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