The degree of copositive approximation by polynomials

Author:
D. Leviatan

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

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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.(to appear). MR**697804 (84f:41022)****[2]**R. A. DeVore,*Monotone approximation by polynomials*, SIAM J. Math. Anal.**8**(1977), 906-921. MR**0510582 (58:23252)****[3]**E. Passow and L. Raymon,*Copositive polynomial approximation*, J. Approx. Theory**12**(1974), 299-304. MR**0355422 (50:7896)****[4]**J. A. Roulier,*The degree of copositive approximation*, J. Approx. Theory**19**(1977), 253-258. MR**0435683 (55:8641)****[5]**-,*Nearly comonotone approximation*, Proc. Amer. Math. Soc.**47**(1975), 84-88. MR**0364967 (51:1220)**

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

Article copyright:
© Copyright 1983
American Mathematical Society