Abstract
We find the exnet value of the best (α, β)-approximation by generalized Chebyshev splines for a class of functions differentiable with weight on [−1, 1].
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References
V. F. Babenko, “Asymmetric approximations in spaces of summable functions.” Ukr. Mat. Zh., 34, No. 4, 409–416 (1982).
N. P. Korneichuk, Exact Constants in the Theory of Approximations [in Russian], Nauka, Moscow, (1987).
S. Karlin and W. J. Studden, Tchebycheff Systems: with Applications in Analysis and Statistics [Russian translation], Nauka, Moscow (1976).
S. Karlin and L. Schumaker, “The fundamental theorem of algebra for Tchebysheffian monosplines,” J. Analyse Math., 5, No. 20, 233–270 (1967).
L. Schumaker, “Uniform approximation by Tchebysheffian spline functions,” J. Math. Mech., 18, No. 4, 369–378 (1968).
A. A. Zhensykbaev, “Chebyshev splines and their properties,” in: Proceedings of the International Conference “Theory of Approximation of Functions” [in Russian], Nauka, Moscow (1987), pp. 164–168.
V. F. Babenko and O. V. Polyakov, “On asymmetric approximations of classes of differentiable functions by splines in the space L 1 [−1, 1],”, in: Optimization of Methods for Approximation [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1992), pp. 27–34.
O. Ya. Shevaldina, “On the approximation of classes W r p by polynomial splines in the mean,” in: Approximation in Special and Abstract Banach Spaces [in Russian], Ural Scientific Center Academy of Sciences of the USSR, Sverdlovsk (1987), pp. 113–120.
V. F. Babenko, “On the existence of perfect splines and monosplines with given zeros,” in: Studies of Contemporary Problems of Summation and Approximation of Functions and Their Applications [in Russian], Dnepropetrovsk University, Dnepropetrovsk. (1987), pp. 6–9.
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Dnepropetrovsk University, Dnepropetrovsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 7, pp. 951–957, July, 1997.
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Polyakov, O.V. Approximation of certain classes of differentiable functions by generalized splines. Ukr Math J 49, 1067–1074 (1997). https://doi.org/10.1007/BF02528752
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DOI: https://doi.org/10.1007/BF02528752