Abstract
We consider inequalities of the Jackson type in the case of approximation of periodic functions by linear means of their Fourier series in the space L 2. In solving this problem, we choose the integral of the square of the modulus of continuity as a majorant of the square of the deviation. We establish that the constants for the Fejér and Rogosinski polynomials coincide with the constant of the best approximation, whereas the constant for the Korovkin polynomials is greater than the constant of the best approximation.
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REFERENCES
L. V. Taikov, “Inequalities for the best approximation and modulus of continuity in L 2,” Mat. Zametki, 20, No.3, 433–438 (1976).
A. A. Ligun, “On some inequalities for the best approximation and modulus of continuity in L 2,” Mat. Zametki, 24, No.6, 785–792 (1978).
P. P. Korovkin, Linear Operators and Approximation Theory[in Russian], Fizmatgiz, Moscow (1959).
A. I. Stepanets, Uniform Approximation by Trigonometric Polynomials[in Russian], Naukova Dumka, Kiev (1981).
S. B. Stechkin, “On some extremal properties of positive trigonometric polynomials,” Mat. Zametki, 7, No.4, 411–423 (1970).
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Bozhukha, L.N. Inequalities of the Jackson Type in the Approximation of Periodic Functions by Fejér, Rogosinski, and Korovkin Polynomials. Ukrainian Mathematical Journal 52, 1818–1825 (2000). https://doi.org/10.1023/A:1010443523764
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DOI: https://doi.org/10.1023/A:1010443523764