An exact estimate in the theory of approximation of the function $x^\alpha$ with Bernstein polynomials in Hausdorff metric

V. At. Kostova

An exact estimate in the theory of approximation of the function $x^{α}$ with Bernstein polynomials in Hausdorff metric

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V. At. Kostova Department of Mathematics TU "Angel Kunchev", Rousse, Bulgaria

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References

Popoviciu, T., Sur l'approximation des fonctions convexes d'ordre supérieur, Mathematica, 10 (1934), pp. 49-54.

Kac, M., Une remarque sur les polynomes de M.S. Bernstein, Studia Math., 7 (1938), pp. 49-51.

Natanson, I. P. Konstruktivnaya teoriya funkciĭ. (Russian) [Constructive Theory of Functions] Gosudarstvennoe Izdatel'stvo Tehniko-Teoretičeskoĭ Literatury, Moscow-Leningrad,] 1949. 688 pp., MR0034464.

Lorentz, G. G. Bernstein polynomials. Mathematical Expositions, no. 8. University of Toronto Press, Toronto, 1953. x+130 pp.,MR0057370.

Sendov, Blagovest H. Order of best Hausdorff polynomial approximation of certain functions. Serdica 1 (1975), no. 1, pp. 77-87, MR0390597.

Sendov, Blagovest Khausdorfovye priblizheniya. (Russian) [Hausdorff approximations] Bolgar. Akad. Nauk, Sofia, 1979. 372 pp., MR0534426.

Popov, Vasil A. Approximation of convex functions by algebraic polynomials in Hausdorff metric. Serdica 1 (1975), no. 3, pp. 386-398, MR0404939.

Strukov, L. I.; Timan, A. F. Mathematical expectation of continuous functions of random variables, smoothness, and variance. (Russian) Sibirsk. Mat. Ž. 18 (1977), no. 3, pp. 658-664, 719, MR0454471.

Kostova, V. At. Approximation of the function xα with Bernstein polynomials in Hausdorff metric. Mathematica (Cluj) 27(52) (1985), no. 2, pp. 141-145, MR0853501.

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Published

1987-08-01

Issue

Vol. 16 No. 2 (1987)

Section

Articles

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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