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How close is the approximation by Bernstein polynomials?

Published online by Cambridge University Press:  08 October 2020

G. J. O. Jameson
G. J. O. Jameson*
Affiliation:
Dept. of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF e-mail: g.jameson@lancaster.ac.uk
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Extract

A famous theorem of Weierstrass, dating from 1885, states that any continuous function can be uniformly approximated by polynomials on a bounded, closed real interval.

Type
Articles
Information
The Mathematical Gazette , Volume 104 , Issue 561 , November 2020 , pp. 482 - 494
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Copyright
© Mathematical Association 2020

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References

Bernstein, S. N., Démonstration du théorème de Weierstrass fondée sur le calcul de probabilités, Comm. Kharkov Math. Soc. 13 (1912).Google Scholar
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Jameson, G. J. O., Monotonicity of weighted averages of convex functions, Math. Ineq. Appl. 23 (2020) pp. 425–432.Google Scholar
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