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A Note on Derivatives of Bernstein Polynomials

✍ Scribed by D.X. Zhou


Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
92 KB
Volume
78
Category
Article
ISSN
0021-9045

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πŸ“œ SIMILAR VOLUMES


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By establishing an identity for \(S_{n}(x):=\sum_{j=0}^{n}|j / n-x|\left({ }_{j}^{n}\right) x^{j}(1-x)^{n-j}\), the present paper shows that a pointwise asymptotic estimate cannot hold for \(S_{n}(x)\), and, at the same time, obtains a better result than that in Bojanic and Cheng [3]. 1993 Academic

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We give an interesting generalization of the Bernstein polynomials. We find sufficient and necessary conditions for uniform convergence by the new polynomials, and we generalize the Bernstein theorem.

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