Literature cited
A. N. Kolmogorov, “Inequalities between the upper bounds of sequences of derivatives of an arbitrary function on an infinite interval,” Uch. Zap. Mosk. Un-ta, Matematika,30, No. 3, 3–13 (1939).
N. P. Korneichuk, “Extreme values of functionals and the best approximations to classes of periodic functions,” Izv. Akad. Nauk SSSR, Ser. Mat.,35, 93–124 (1971).
E. G. Gol'shtein, The Theory of Duality in Mathematical Programming and its Applications [in Russian], Nauka, Moscow (1971).
A. A. Ligun, “Precise constants in Jackson and Kolmogorov type inequalities,” Dissertation, Dnepropetrovsk (1974).
V. G. Doronin and A. A. Ligun, “The best one-sided approximation to one class of functions by another,” Matem. Zametki,14, No. 5, 627–632 (1973).
V. G. Doronin and A. A. Ligun, “The best one-sided approximation to several classes of continuous functions,” in: A Study of Modern Problems of Summation and Approximation to Functions, and Their Applications, 5, Dnepropetrovsk State Univ., 42–49 (1974).
G. Hardy, L. Littlewood, and G. Polya, Inequalities, Cambridge (1934).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 20, No. 3, pp. 417–424, September, 1976.
Rights and permissions
About this article
Cite this article
Doronin, V.G., Ligun, A.A. Precise values of the best one-sided approximations by splines. Mathematical Notes of the Academy of Sciences of the USSR 20, 789–793 (1976). https://doi.org/10.1007/BF01097252
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01097252