The degree of copositive approximation by polynomials

Author:
D. Leviatan

Journal:
Proc. Amer. Math. Soc. **88** (1983), 101-105

MSC:
Primary 41A29; Secondary 41A25

MathSciNet review:
691286

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Abstract: Jackson type theorems are established for the approximation of a function that changes sign finitely many times in by polynomials which are copositive with it . The results yield the rate of nonconstrained approximation and are thus best possible in the same sense as in the nonconstrained case.

**[1]**R. K. Beatson and D. Leviatan,*On comonotone approximation*, Canad. Math. Bull.**26**(1983), no. 2, 220–224. MR**697804**, 10.4153/CMB-1983-034-0**[2]**Ronald A. DeVore,*Monotone approximation by polynomials*, SIAM J. Math. Anal.**8**(1977), no. 5, 906–921. MR**0510582****[3]**Eli Passow and Louis Raymon,*Copositive polynomial approximation*, J. Approximation Theory**12**(1974), 299–304. MR**0355422****[4]**John A. Roulier,*The degree of copositive approximation*, J. Approximation Theory**19**(1977), no. 3, 253–258. MR**0435683****[5]**John A. Roulier,*Nearly comonotone approximation*, Proc. Amer. Math. Soc.**47**(1975), 84–88. MR**0364967**, 10.1090/S0002-9939-1975-0364967-8

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DOI:
https://doi.org/10.1090/S0002-9939-1983-0691286-7

Article copyright:
© Copyright 1983
American Mathematical Society