Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Derivatives of Bernstein polynomials and smoothness


Author: Z. Ditzian
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 41A10

Retrieve articles in all journals with MSC: 41A10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0766520-7
Keywords: Bernstein polynomial, moduli of smoothness
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society