Derivatives of Bernstein polynomials and smoothness
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- by Z. Ditzian PDF
- Proc. Amer. Math. Soc. 93 (1985), 25-31 Request permission
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.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 25-31
- MSC: Primary 41A10
- DOI: https://doi.org/10.1090/S0002-9939-1985-0766520-7
- MathSciNet review: 766520