Geodesic
Approximation of Boltsano Function by Means of Bernstein Polynomials
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 1, pp. 56-59 Cet article a éte moissonné depuis la source Math-Net.Ru

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In given work is considered Boltsano function $f(x)$, which can be represented in rows. Boltsano function is continuous and not differentiable. It is received the estimation of the module of continuity of Boltsano function. From the estimation of the module of continuity follows that function $f(x)$ belongs to the Lipschitz class $\mathrm{Lip}\,1/2$ with the constant 6, i. e. $f(x)\in 6\,\mathrm{Lip}\,1/2$. For the Boltsano function for $a=1$ and $h=1$ it is presented the sequence of Bernstein polynomials and it is proved the estimation of the error of approximation for Boltsano function by means of Bernstein polynomials. 
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I. A. Kozlova. Approximation of Boltsano Function by Means of Bernstein Polynomials. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 1, pp. 56-59. http://geodesic.mathdoc.fr/item/ISU_2013_13_1_a13/

[1] Brzhechka B. F., “About the function of Bolzano”, Russ. Math. Surv., 4:2 (1949), 329–346 | MR

[2] Privalov A. A., Theory interpolate functions, v. 1, Izd-vo Saratov. un-ta, Saratov, 1990, 231 pp. | MR