On the extension of differentiable functions from their monotonicity interval and inequalities of Kolmogorov type
Abstract
We study the possibility of extension for every function $$$f\in L_{\infty}(\mathbb{R})$$$ from any monotonicity interval $$$I$$$ of function $$$f$$$ to the whole axis with retaining norms of $$$f$$$ and $$$f^{(r)}$$$ on interval.
Keywords
Kolmogorov-type inequalities; the comparison theorem of Kolmogorov
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Babenko V.F., Kofanov V.A., Pichugov S.A. "Exact constants of Kolmogorov type with bounded higher derivative in case of small smoothness", Ukrainian Math. J., 2001; 53(10): pp. 1298-1308.
Babenko V.F., Korneichuk N.P., Kofanov V.A., Pichugov S.A. Inequalities for derivatives and their applications, Naukova dumka, 2003.
Kolmogorov A.N. "On inequalities between upper bounds of consecutive derivatives of the function on infinite interval", Izbr. tr. Matematika, mekhanika, Nauka, 1985; pp. 252-263.
DOI: https://doi.org/10.15421/241406
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Copyright (c) 2014 Yu.S. Zagorul'ko, V.A. Kofanov
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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
