Geodesic
On the rate of approximation of functions by the Bernstein polynomials
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 3, pp. 162-169

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The estimates are refined for the deviations of the Bernstein polynomials from functions at a fixed point and for the remainders in the asymptotic formulas for these deviations for differentiable functions. 
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     author = {S. A. Telyakovskii},
     title = {On the rate of approximation of functions by the {Bernstein} polynomials},
     journal = {Trudy Instituta matematiki i mehaniki},
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S. A. Telyakovskii. On the rate of approximation of functions by the Bernstein polynomials. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 3, pp. 162-169. http://geodesic.mathdoc.fr/item/TIMM_2008_14_3_a14/