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Convexity and variation diminishing property for Bernstein polynomials in higher dimensions. (English) Zbl 0689.41006

Approximation and function spaces, Proc. 27th Semest., Warsaw/Pol. 1986, Banach Cent. Publ. 22, 45-53 (1989).
[For the entire collection see Zbl 0681.00013.]
Necessary and sufficient conditions for the convexity of the Bézier net over a k-dimensional simplex are presented. Multidimensional versions of the variational diminishing property of Bernstein polynomials are also considered.
Reviewer: M.Beśka

MSC:

41A10 Approximation by polynomials
41A36 Approximation by positive operators

Citations:

Zbl 0681.00013