Geodesic
Approximation by Bernstein polynomials at the discontinuity points of derivatives
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and differential equations, Tome 269 (2010), pp. 265-270.

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We obtain asymptotic formulas for the deviation of Bernstein polynomials from functions at the first-kind discontinuity points of the highest derivatives of odd order. 
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V. O. Tonkov. Approximation by Bernstein polynomials at the discontinuity points of derivatives. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and differential equations, Tome 269 (2010), pp. 265-270. http://geodesic.mathdoc.fr/item/TM_2010_269_a21/

[1] Lorentz G.G., Bernstein polynomials, 2nd ed., Chelsea Publ., New York, 1986 | MR | Zbl

[2] Chlodovsky I., “Sur la représentation des fonctions discontinues par les polynomes de M. S. Bernstein”, Fund. math., 13 (1929), 62–72

[3] Telyakovskii S.A., “O priblizhenii mnogochlenami Bernshteina v tochkakh razryva proizvodnykh”, Mat. zametki, 85:4 (2009), 622–629 | DOI | MR | Zbl

[4] Telyakovskii S.A., “O priblizhenii differentsiruemykh funktsii mnogochlenami Bernshteina i mnogochlenami Kantorovicha”, Tr. MIAN, 260, 2008, 289–296 | MR | Zbl