Monotone and comonotone approximation
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- by E. Passow and L. Raymon
- Proc. Amer. Math. Soc. 42 (1974), 390-394
- DOI: https://doi.org/10.1090/S0002-9939-1974-0336176-9
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Abstract:
Jackson type theorems are obtained for monotone and comonotone approximation. Namely (i) If $f(x)$ is a function such that the kth difference of f is $\geqq 0$ on [a, b] then the degree of approximation of f by nth degree polynomials with kth derivative $\geqq 0$ is $0[\omega (f;1/{n^{1 - \varepsilon }})]$ for any $\varepsilon > 0$, where $\omega (f;\delta )$ is the modulus of continuity of f on [a, b]. (ii) If $f(x)$ is piecewise monotone on [a, b] then the degree of approximation of f by nth degree polynomials comonotone with f is $0[\omega (f;1/{n^{1 - \varepsilon }})]$ for any $\varepsilon > 0$.References
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Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 390-394
- MSC: Primary 41A50
- DOI: https://doi.org/10.1090/S0002-9939-1974-0336176-9
- MathSciNet review: 0336176