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Derivatives of Bernstein polynomials and smoothness

Author: Z. Ditzian
Journal: Proc. Amer. Math. Soc. 93 (1985), 25-31
MSC: Primary 41A10
MathSciNet review: 766520
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Abstract: Equivalence relations between the asymptotic behaviour of derivatives of Bernstein polynomials and the smoothness of the function they approximate are given. This is achieved with an a priori condition that the function is of class $ \operatorname{Lip}\beta $ with some small $ \beta > 0$. The a priori condition is dropped when a similar equivalence relation using the Katorovich operator is proved.

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Keywords: Bernstein polynomial, moduli of smoothness
Article copyright: © Copyright 1985 American Mathematical Society