Beśka, Marek 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 Keywords:Laplace operator; Bézier net; Bernstein polynomials Citations:Zbl 0681.00013 PDFBibTeX XML