Literature Cited
G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge Univ. Press (1964).
N. P. Korneichuk, A. A. Ligun, and V. G. Doronin, Approximations with Constraints [in Russian], Naukova Dumka, Kiev (1982).
N. P. Korneichuk, “Extremal values of functionals and best approximation on classes of periodic functions,” Izv. Akad. Nauk SSSR, Ser. Mat.,35, No. 1, 93–124 (1971).
N. P. Korneichuk, Extremal Problems of Approximation Theory [in Russian], Nauka, Moscow (1976).
N. P. Korneichuk, “On the approximation of functions and their derivatives by interpolation splines,” Dokl. Akad. Nauk SSSR,264, No. 5, 1063–1066 (1982).
S. B. Stechkin and Yu. N. Subbotin, Splines in Numerical Mathematics [in Russian], Nauka, Moscow (1986).
Yu. S. Zav'yalov, B. I. Kvasov, and V. L. Miroshnichenko, Methods of Spline-Functions [in Russian], Nauka, Moscow (1980).
J. H. Ahlberg, E. N. Nilson, and J. L. Walsh, The Theory of Splines and Their Applications, Academic Press, New York (1967).
M. V. Golitschek, “On n-widths and interpolation by polynomial splines,” J. Approx. Theory,26, 133–141 (1979).
A. A. Zhensykbaev, “Approximation of differentiable periodic functions by splines on a uniform subdivision,” Mat. Zametki,13, No. 6, 807–816 (1973).
C. A. Hall and W. W. Meyer, “Optimal error bounds for cubic spline interpolation,” J. Approx. Theory,16, 105–122 (1976).
V. M. Tikhomirov, “The best methods of approximation and interpolation of differentiable functions in the space C[−1, 1],” Mat. Sb.,80, No. 2, 290–304 (1969).
A. A. Ligun, “On the widths of certain classes of differentiable periodic functions,” Mat. Zametki,27, No. 1, 61–75 (1980).
N. P. Korneichuk, “Best approximation by splines on classes of periodic functions in the metric of L,” Mat. Zametki,20, No. 5, 655–664 (1976).
V. I. Ruban, “The widths of sets in spaces of periodic functions,” Dokl. Akad. Nauk SSSR,255, No. 1, 34–35 (1980).
A. A. Zhensykbaev, “Spline-interpolation and the best approximation by trigonometric polynomials,” Mat. Zametki,26, No. 3, 355–366 (1979).
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 24, No. 5, pp. 94–108, September–October, 1983.
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Korneichuk, N.P. Certain sharp inequalities for differentiable functions and estimation of approximation of functions and their derivatives by cubic interpolation splines. Sib Math J 24, 723–735 (1983). https://doi.org/10.1007/BF00969599
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DOI: https://doi.org/10.1007/BF00969599