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Bernstein Power Series

Published online by Cambridge University Press:  20 November 2018

E. W. Cheney  and
A. Sharma
E. W. Cheney
Affiliation:
University of California, Los Angeles and University of Alberta, Calgary
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 241 - 252
Copyright
Copyright © Canadian Mathematical Society 1964

References

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