Abstract
From previously published results of the author on the exact upper bound of best approximations by trigonometric polynomials for classes of periodic differentiable functions are derived the values of the exact constants in Jackson's inequalities for 2π-periodic functionsfε Cr with modulus of continuity ω(f (r); t) for the r-th derivative which is convex upwards.
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N. P. Korneichuk, “The exact constant in Jackson's theorem on the best uniform, approximation of continuous periodic functions,” Dokl. Akad. Nauk SSSR,145, No. 3, 514–515 (1962).
V. V. Zhuk, “Some relations between moduli of continuity and functionals defined on a set of periodic functions,” Izv. Vuzov, Matematika, No. 5, 24–33 (1970).
N. P. Korneichuk, “Extremal values of functionals and the best approximation for classes of periodic functions,” Izv. Akad. Nauk SSSR, Ser. Matem.,35, No. 1, 93–124 (1971).
A. V. Efimov, “Linear approximation methods for continuous periodic functions,” Matem. Sb.,54(96), No. 1, 51–90 (1961).
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Translated from Matematicheskie Zametki, Vol. 12, No. 5, pp. 517–522, November, 1972.
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Korneichuk, N.P. A note on Jackson's theorem for differentiable functions. Mathematical Notes of the Academy of Sciences of the USSR 12, 747–750 (1972). https://doi.org/10.1007/BF01099057
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DOI: https://doi.org/10.1007/BF01099057