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Proceedings of the American Mathematical Society

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

 

 

Negative theorems on monotone approximation


Author: John A. Roulier
Journal: Proc. Amer. Math. Soc. 55 (1976), 37-43
DOI: https://doi.org/10.1090/S0002-9939-1976-0393969-1
MathSciNet review: 0393969
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Abstract: In this paper we show that for $ f$ continuous on $ [ - 1, + 1]$ and satisfying $ (f({x_2}) - f({x_1}))/({x_2} - {x_1}) \geqq \delta > 0$, it is possible to have infinitely many of the polynomials of best uniform approximation to $ f$ not increasing on $ [ - 1, + 1]$.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0393969-1
Article copyright: © Copyright 1976 American Mathematical Society