Comonotone approximation
Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 2, pp. 319-363.

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All cases of the validity of classic pointwise and uniform estimates of unconstrained polynomial approximation are investigated for piecewise monotone approximation.
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J. Gilewicz; I. A. Shevchuk. Comonotone approximation. Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 2, pp. 319-363. http://geodesic.mathdoc.fr/item/FPM_1996_2_2_a0/