Results 151 to 160 of about 1,549 (180)

On an inequality of the Kolmogorov type for a second-order differential expression

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1993
Abstract In this paper we discuss an integro-differential inequality formed from the square of a second-order differential expression. A connection between the existence of the inequality and the Titchmarsh–Weyl m-function is established and it is shown that the best constant in the inequality is determined by the behaviour of the m ...
Beynon, M. J., Brown, B. M., Evans, W. D.   +2 more
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On the connection between certain inequalities of the Kolmogorov type for periodic and nonperiodic functions

Ukrainian Mathematical Journal, 1999
Summary: Nonperiodic analogs are obtained of the known inequalities which estimate \(L_{p}\)-norms of intermediate derivatives of a periodic function in terms of \(L_{\infty}\)-norms and the higher derivative of the considered function.
Babenko, V. F., Selivanova, S. A.
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Kolmogorov-type inequalities for mixed derivatives of functions of many variables

Ukrainian Mathematical Journal, 2004
Let γ = (γ1,...,γ d ) be a vector with positive components and let Dγ be the corresponding mixed derivative (of order γ j with respect to the jth variable). In the case where d > 1 and 0 < k < r are arbitrary, we prove that
V. F. Babenko, N. P. Korneichuk, S. A. Pichugov   +2 more
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Sharp Kolmogorov–Remez-Type Inequalities for Periodic Functions of Low Smoothness

Ukrainian Mathematical Journal, 2020
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On inequalities of Kolmogorov-Hörmander type for functions bounded on a discrete net

Ukrainian Mathematical Journal, 1997
Let \(L_{\infty}^{r}(\mathbb{R})\) be the space of functions \(f(x)\) which have locally absolutely continuous derivatives \(f^{(r-1)}(x)\) and a derivative \(f^{(r)}(x)\) such that \(\|f^{(r)}\|_{\infty}0\) and \(S_{\varepsilon}\) be some uniform net on \(\mathbb{R}\) with step \(\varepsilon.\) For \(f\in L_{\infty}(\mathbb{R})\) set \(\|f\|_{S_ ...
Babenko, V. F., Vakarchuk, M. B.
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One Inequality of the Landau–Kolmogorov Type for Periodic Functions of Two Variables

Ukrainian Mathematical Journal, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Kolmogorov-Type Inequalities Taking into Account the Number of Changes in the Sign of Derivatives

Ukrainian Mathematical Journal, 2003
New exact Kolmogorov-type inequalities \[ \| x^{(k)}\| _q\leq \left(\frac{\nu(x^{(k)})}{2}\right)^{1/q} \frac{\| \varphi_{r-k}\| _q}{| | | \varphi_r| | | _p^\alpha} | | | x| | | _p^\alpha\| x^{(r)}\| _\infty^{1-\alpha},\;q\in [1,\infty],\;p\in (0,\infty], \;k,r\in {\mathbb N ...
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Relationship Between the Bojanov–Naidenov Problem and the Kolmogorov-Type Inequalities

Ukrainian Mathematical Journal
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Pointwise Inequalities of Landau–Kolmogorov Type for Functions Defined on a Finite Segment

Ukrainian Mathematical Journal, 2001
For arbitrary \(t\in [0,1]\), \(p\in [1,\infty ]\) and \(A\geq 2\) the author finds the best possible constant \(B\) in the inequality \[ |x'(t)|\leq A\|x\|_{L_\infty [0,1]}+B\|x''\|_{L_p(0,1)}. \] This leads to the precise inequality for the norms \[ \|x'\|_\infty \leq \frac{2}{h}\|x\|_\infty +\left( \frac{h}{p'+1}\right)^{1/p'}\|x''\|_p \] valid for ...
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Bessel type Kolmogorov inequalities on weighted Lebesgue spaces

Applicable Analysis, 2021
Ismail Ekincioglu, Esra Kaya
exaly