The paper considers strong approximation of continuous functions by positive operators. Estimates in terms of the modulus of continuity and its convex majorant are established. Bibliography: 4 titles.
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V. Zhuk and G. Natanson, “To the question of approximating functions by positive operators,” Uchen. Zap. Tartus. Gos. Univ., 430, 58–69 (1977).
V. I. Zubov, “Bernstein interpolation polynomials,” Dokl. RAN, 343, No. 5, 593–595 (1955).
V. V. Zhuk, Structural Properties of Functions and Approximation Accuracy [in Russian], Leningrad (1984).
I. K. Daugavet, Introduction to the Classical Theory of Function Approximation [in Russian], St.Petersburg (2011).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 440, 2015, pp. 68–80.
Translated by L. Yu. Kolotilina.
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Zhuk, V.V. Strong Approximation of Functions by Positive Operators. J Math Sci 217, 45–53 (2016). https://doi.org/10.1007/s10958-016-2954-3
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DOI: https://doi.org/10.1007/s10958-016-2954-3