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2007/2008 Are the Kantorovitch Polynomials Area Diminishing?
Martin E. Price
Real Anal. Exchange 33(1): 235-246 (2007/2008).


The Bernstein-Bezier polynomials are known to possess total variation and length diminishing properties in one variable. We investigate the two dimensional generalizations to the square and the triangle. Simple counterexamples show that they do not diminish surface area. We consider Kantorovitch polynomials which seem to be a better choice to be area diminishing. A counterexample is given for the square. We then define the Kantorovitch polynomials on the triangle and give an area estimate for them.


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Martin E. Price. "Are the Kantorovitch Polynomials Area Diminishing?." Real Anal. Exchange 33 (1) 235 - 246, 2007/2008.


Published: 2007/2008
First available in Project Euclid: 28 April 2008

zbMATH: 1151.41006
MathSciNet: MR2402875

Primary: 26B15 , 41A10

Keywords: Bernstein polynomial , Kantorovitch Polynomials , surface area

Rights: Copyright © 2007 Michigan State University Press

Vol.33 • No. 1 • 2007/2008
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