Geodesic
On the order of an~approximation of functions on sets of positive measure by linear positive polynomial operators
Matematičeskie zametki, Tome 13 (1973) no. 3, pp. 457-468.

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It is proved that at almost all points the order of approximation, even of one of the functions 1, $\cos x$, $\sin x$ by means of a sequence of linear positive polynomial operators having uniformly bounded norms, is not higher than $1/n^2$. Refinements of this result are given for operators of convolution type. 
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     author = {R. K. Vasil'ev},
     title = {On the order of an~approximation of functions on sets of positive measure by linear positive polynomial operators},
     journal = {Matemati\v{c}eskie zametki},
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R. K. Vasil'ev. On the order of an~approximation of functions on sets of positive measure by linear positive polynomial operators. Matematičeskie zametki, Tome 13 (1973) no. 3, pp. 457-468. http://geodesic.mathdoc.fr/item/MZM_1973_13_3_a16/