Abstract
The paper studies approximations of functions defined on the entire number axis and bounded on any finite segment, the approximations being by V. A. Steklov functions in Hausdorff metric. We obtain the value of the exact upper bound of the approximation on classes of functions of given majorant of their moduli of nonmonotonicity.
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VI. Sendov, “Approximations by step functions relative to Hausdorff distance,” Matem. Zametki,2, No. 1, pp. 61–70 (1967).
VI. Sendov, “On the theorems of P. P. Korovkin for the convergence of sequences of linear positive operators,” Dokl. Akad. Nauk SSSR,177, No. 3, pp. 518–520 (1967).
VI. Sendov, “Linear methods of approximating periodic functions relative to a Hausdorff-type metric,” Dokl. Akad. Nauk SSSR,160, No. 5, pp. 1023–1025 (1965).
N. I. Akhiezer, Lectures on Approximation Theory [in Russian], Moscow-Leningrad (1947).
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Translated from Matematicheskie Zametki, Vol. 5, No. 1, pp. 21–30, January 1969.
The author wishes to express his gratitude to N. P. Korneichuk under whose direction this paper was prepared.
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Martynyuk, V.T. Approximations by V. A. Steklov functions in Hausdorff metric. Mathematical Notes of the Academy of Sciences of the USSR 5, 15–20 (1969). https://doi.org/10.1007/BF01098709
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DOI: https://doi.org/10.1007/BF01098709