Geodesic
Negative Results in Form-Preserving Approximation of Higher Order
Matematičeskie zametki, Tome 76 (2004) no. 6, pp. 812-823.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that for $q$-convex polynomial approximations, where $q\ge4$ , inequalities of Jackson type are not valid even with a constant depending on the approximated function. 
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A. V. Bondarenko; A. V. Primak. Negative Results in Form-Preserving Approximation of Higher Order. Matematičeskie zametki, Tome 76 (2004) no. 6, pp. 812-823. http://geodesic.mathdoc.fr/item/MZM_2004_76_6_a1/

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