The paper proves that,if f（x）∈Lp[-1,1 ≤ p ＜ ∞,changes sign l times in（-1,1）,-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 ‖f-r‖p≤Cδl2μω holds,where μ is a natural nuωmber ≥（3/2）+（1/p）,and Cδ is a positive constant depending only on δ.
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