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Almost Copositive Polynomial Approximation
Dr. Eman Samir Bhaya, Department of Mathematics, College of Education,
Babylon University, Babil, Hilla, Iraq.
E.mail: emanbhaya@yahoo.com
Abstract
For a function with finitely many sign changes, Hu, Kopotun and Yu [5] construct a sequence of polynomials which are copositive with this function in terms of the Ditzian-Totik modulus of continuity in lp, p<1 metric. Also it was shown that this estimate is exact in the sense that if has at least one sign change then w can not be replaced by w3 if .
In this paper we first show that almost copositive approximation improves the rate to w3 from w the rate for the ordinary copositive approximation. Our second theorem shows that it is impossible to obtain the first estimate interims of .
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