Some Properties of Bernstein Polynomials on a Simples
Received:June 20, 1992  
Key Words: Bernstein polynomial   integral coefficient   derivative approximation  
Fund Project:
Author NameAffiliation
Wu Shuntang Dept . of Math.
Zhenjiang Teacherls College Zhenjiang
Jiangsu 212003
Hong Dong Dept. of Math.
Texas A & M University
College Station
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      Let Bn(f,) be the Bernstein polynomial of degree n for a continuous functionf with respect to a d-dimensional simplex σ. In this paperi the approximiation error ofpartial derivatives of f by the partial derivatives of Bn(f,) for f ∈ Cr(σ) and for f ∈Cr+2(σ) are obtained. Also, the approximation, in Lp- norm, by the partial derivativesof Bernstein polynomials with integral coefficients on the simplex is considered.
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