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 Mat. Zametki, 2008, Volume 84, Issue 4, Pages 583–594 (Mi mz4103)

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

DOI: https://doi.org/10.4213/mzm4103

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English version:
Mathematical Notes, 2008, 84:4, 544–554

Bibliographic databases:

UDC: 517.518

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

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz4103
• https://doi.org/10.4213/mzm4103
• http://mi.mathnet.ru/eng/mz/v84/i4/p583

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. V. Mironenko, “On the estimate of the uniform deviation from the class of functions with bounded third derivative”, Proc. Steklov Inst. Math. (Suppl.), 264, suppl. 1 (2009), S168–S176
2. A. V. Mironenko, “On the Jackson–Stechkin inequality for algebraic polynomials”, Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S116–S123
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