Nearly comonotone approximation

Roulier, John A.

doi:10.1090/S0002-9939-1975-0364967-8

Nearly comonotone approximation
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Proc. Amer. Math. Soc. 47 (1975), 84-88 Request permission

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.

References

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