Abstract
The paper studies the problem of uniform approximation of a continuous function on a closed interval by the class of functions with bounded second derivative. We prove an estimate of the value of best approximation of the function by this class via its second modulus of continuity. The obtained estimate is sharp for the class of continuous functions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. V. Mironenko, “Uniform approximation by the class of functions with bounded derivative,” Mat. Zametki 74(5), 696–712 (2003) [Math. Notes 74 (5–6), 656–670 (2003)].
A. V. Mironenko, “An estimate for the least uniform deviation from the class of functions with bounded second derivative,” Sibirsk. Mat. Zh. 47(4), 842–858 (2006) [Siberian Math. J. 47 (4), 696–709 (2006)].
A. V. Mironenko, “On the sharpness of estimates for approximation by the class of functions with bounded the second derivative,” Sibirsk. Mat. Zh. 48(6), 1285–1294 (2007) [Siberian Math. J. 48 (6), 1029–1037 (2007)].
N. P. Korneichuk, Exact Constants in Approximation Theory (Nauka, Moscow, 1987) [in Russian].
V. F. Dem’yanov and V. N. Malozemov, Introduction to Minimax (Nauka, Moscow, 1972) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A. V. Mironenko, 2008, published in Matematicheskie Zametki, 2008, Vol. 84, No. 4, pp. 583–594.
Rights and permissions
About this article
Cite this article
Mironenko, A.V. Approximation by the class of functions with bounded second derivative. Math Notes 84, 544–554 (2008). https://doi.org/10.1134/S0001434608090265
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0001434608090265