Constants in the Jackson theorem

D. Jackson, Über die Genauigkeit der Annäherung Stetiger Funktionen durch Ganze Rational Funktionunes Gegebenes Grades and Trigonometrische Summen Gegebener Ordung, Dissertation, Gottingen (1911). N. P. Korneichuk, “On the best uniform approximation on certain classes of continuous functions,” Dokl. Akad. Nauk SSSR,140, 748–751 (1971). N. I. Chernykh, “On the Jackson inequality in L2,” Tr. Mat. Inst. Akad. Nauk SSSR,88, 71–74 (1967). V. V. Zhuk, “Certain sharp inequalities between uniform approximations of periodic functions,” Dokl. Akad. Nauk SSSR,201, 263–266 (1967). A. A. Ligun, “On the exact constants of approximation of differentiable periodic functions,” Mat. Zametki,14, No. 1, 21–30 (1973). N. P. Korneichuk [N. P. Korneičuk], “Approximation of periodic functions by spline functions,” in: Fourier Analysis and Approximation Theory, G. Alexits and Pál Turán (eds.) Vol. II, North-Holland, Amsterdam (1978), pp. 465–471. A. A. Ligun, “Exact constants in Jackson and Kolmogorov type inequalities,” Author's Abstract of Candidate's Dissertation, Dnepropetrovsk (1974). N. P. Korneichuk, Extremal Problems of Approximation Theory [in Russian], Nauka, Moscow (1976). N. P. Korneichuk, “A remark on the Jackson theorem for differentiable functions,” Mat. Zametki,12, No. 5, 517–522 (1972). G. H. Hardy, D. E. Littlewood, and G. Pólya, Inequalities, Cambridge Univ. Press (1964). V. T. Gavrilyuk, “Approximation of continuous periodic functions by trigonometric poly-nomials,” in: Theory of Approximation of Functions and Its Applications [in Russian], V. K. Dzyadik and V. T. Gavarilyuk (eds.), Izd. Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1974), pp. 41–60. A. N. Davidchuk and A. A. Ligun, “On the Jackson theorem,” Mat. Zametki,14, No. 5, 681–689 (1973). V. F. Babenko and V. V. Shalaev, “On the inequalities of the type of Jackson inequalities for the linear methods of approximation of functions,” Dokl. Akad. Nauk Ukr. SSR,10, 31–34 (1980). V. M. Tikhomirov, Certain Problems of Approximation Theory [in Russian], Moscow State Univ. (1976).