Geodesic
Approximation by Bernstein Polynomials at the Points of Discontinuity of the Derivatives
Matematičeskie zametki, Tome 85 (2009) no. 4, pp. 622-629

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

It is proved that, in the asymptotic formulas for the deviations of Bernstein polynomials from functions at the points of discontinuity of the first kind of the highest even-order derivative, the value of such a derivative can be replaced by the half-sum of its limits on the right and on the left.
Keywords: Bernstein polynomial, Peano derivative, point of discontinuity of the first kind, Stirling's formula, modulus of continuity. 
S. A. Telyakovskii. Approximation by Bernstein Polynomials at the Points of Discontinuity of the Derivatives. Matematičeskie zametki, Tome 85 (2009) no. 4, pp. 622-629. http://geodesic.mathdoc.fr/item/MZM_2009_85_4_a11/
@article{MZM_2009_85_4_a11,
     author = {S. A. Telyakovskii},
     title = {Approximation by {Bernstein} {Polynomials} at the {Points} of {Discontinuity} of the {Derivatives}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {622--629},
     year = {2009},
     volume = {85},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_85_4_a11/}
}
TY  - JOUR
AU  - S. A. Telyakovskii
TI  - Approximation by Bernstein Polynomials at the Points of Discontinuity of the Derivatives
JO  - Matematičeskie zametki
PY  - 2009
SP  - 622
EP  - 629
VL  - 85
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_2009_85_4_a11/
LA  - ru
ID  - MZM_2009_85_4_a11
ER  - 
%0 Journal Article
%A S. A. Telyakovskii
%T Approximation by Bernstein Polynomials at the Points of Discontinuity of the Derivatives
%J Matematičeskie zametki
%D 2009
%P 622-629
%V 85
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_2009_85_4_a11/
%G ru
%F MZM_2009_85_4_a11

[1] G. G. Lorentz, Bernstein Polynomials, Chelsea Publ., New York, 1986 | MR | Zbl

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

[3] G. M. Fikhtengolts, Kurs differentsialnogo i integralnogo ischisleniya, T. 2, Fizmatlit, M., 2002 | MR | Zbl

[4] S. A. Telyakovskii, “O priblizhenii differentsiruemykh funktsii mnogochlenami Bernshteina i mnogochlenami Kantorovicha”, Teoriya funktsii i nelineinye uravneniya v chastnykh proizvodnykh, Tr. MIAN, 260, Nauka, M., 2008, 289–296