Copositive approximation by rational functions with prescribed numerator degree

The paper proves that, if f(x) ∈ L[−1,1]p, 1 ≤ p < ∞, changes sign l times in (−1, 1), then there exists a real rational function r(x) ∈ Rn(2μ−1)l which is copositive with f(x), such that the following Jackson type estimate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left\| {f - r} \right\|_p \leqslant C_\delta l^{2\mu } \omega _\rho \left( {f,\frac{1} {n}} \right)_p $$\end{document} holds, where μ is a natural number ≥ 3/2 + 1/p, and Cδ is a positive constant depending only on δ.