Bernstein Power Series

In Bernstein's proof of the Weierstrass Approximation Theorem, the polynomials are constructed in correspondence with a function f ∊ C [0, 1] and are shown to converge uniformly to f. These Bernstein polynomials have been the starting point of many investigations, and a number of generalization...

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Bibliographic Details
Published in:Canadian journal of mathematics 1964, Vol.16, p.241-252
Main Authors: Cheney, E. W., Sharma, A.
Format: Article
Language:English
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Summary:In Bernstein's proof of the Weierstrass Approximation Theorem, the polynomials are constructed in correspondence with a function f ∊ C [0, 1] and are shown to converge uniformly to f. These Bernstein polynomials have been the starting point of many investigations, and a number of generalizations of them have appeared. It is our purpose here to consider several generalizations in the form of infinite series and to establish some of their properties.
ISSN:0008-414X
1496-4279
DOI:10.4153/CJM-1964-023-1