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This article is cited in 2 scientific papers (total in 2 papers)
Approximation by the Class of Functions with Bounded Second Derivative
A. V. Mironenko Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
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.
Keywords:
continuous function, best approximation of a function, modulus of continuity, alternance, spline, absolutely continuous function, Lipschitz function, divided difference.
Received: 16.04.2007
Citation:
A. V. Mironenko, “Approximation by the Class of Functions with Bounded Second Derivative”, Mat. Zametki, 84:4 (2008), 583–594; Math. Notes, 84:4 (2008), 544–554
Linking options:
https://www.mathnet.ru/eng/mzm4103https://doi.org/10.4213/mzm4103 https://www.mathnet.ru/eng/mzm/v84/i4/p583
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Abstract page: | 388 | Full-text PDF : | 207 | References: | 64 | First page: | 4 |
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