The degree of copositive approximation by polynomials
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- by D. Leviatan
- Proc. Amer. Math. Soc. 88 (1983), 101-105
- DOI: https://doi.org/10.1090/S0002-9939-1983-0691286-7
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Abstract:
Jackson type theorems are established for the approximation of a function $f$ that changes sign finitely many times in $[ - 1,1]$ by polynomials ${p_n}$ which are copositive with it $f{p_n} \geqslant 0{\text { on }}[ - 1,1]$. The results yield the rate of nonconstrained approximation and are thus best possible in the same sense as in the nonconstrained case.References
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- Eli Passow and Louis Raymon, Copositive polynomial approximation, J. Approximation Theory 12 (1974), 299–304. MR 355422, DOI 10.1016/0021-9045(74)90071-9
- John A. Roulier, The degree of copositive approximation, J. Approximation Theory 19 (1977), no. 3, 253–258. MR 435683, DOI 10.1016/0021-9045(77)90056-9
- John A. Roulier, Nearly comonotone approximation, Proc. Amer. Math. Soc. 47 (1975), 84–88. MR 364967, DOI 10.1090/S0002-9939-1975-0364967-8
Bibliographic Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 88 (1983), 101-105
- MSC: Primary 41A29; Secondary 41A25
- DOI: https://doi.org/10.1090/S0002-9939-1983-0691286-7
- MathSciNet review: 691286