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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Nearly comonotone approximation


Author: John A. Roulier
Journal: Proc. Amer. Math. Soc. 47 (1975), 84-88
MSC: Primary 41A25
MathSciNet review: 0364967
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Abstract: This paper obtains estimates on the degree of nearly comonotone approximation which extend and improve the estimate obtained by Newman, Passow, and Raymon. In particular, the restriction that $ f \in {\operatorname{Lip} _M}1$ is removed, and estimates for the degree of nearly comonotone approximation are obtained for all proper piecewise monotone functions. It is also shown that if $ f'$ exists and is continuous on the interval, then the ordinary polynomials of best approximation form a nearly comonotone sequence.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0364967-8
PII: S 0002-9939(1975)0364967-8
Article copyright: © Copyright 1975 American Mathematical Society