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A kind of sharp Wirtinger inequalities
International Journal of Wavelets, Multiresolution and Information Processing, 2023This study gives a kind of sharp Wirtinger inequalities (Pizone inequalities) [Formula: see text] where [Formula: see text] with at least [Formula: see text] zeros (counting multiplicity) in [Formula: see text]. First, based on the Hermite (Lagrange) interpolation, we express [Formula: see text] as a Lagrange type (integral type) remainder. Second, we
Guiqiao Xu, Yongping Liu, Dandan Guo
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Wirtinger's Inequalities on Time Scales
Canadian Mathematical Bulletin, 2008AbstractThis paper is devoted to the study of Wirtinger-type inequalities for the Lebesgue Δ-integral on an arbitrary time scale 𝕋. We prove a general inequality for a class of absolutely continuous functions on closed subintervals of an adequate subset of 𝕋.
Ravi P. Agarwal +3 more
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GENERALIZATIONS OF THE WIRTINGER–NORTHCOTT INEQUALITY
Bulletin of the London Mathematical Society, 2003For \(2\pi\)-periodic functions satisfying \(\int^{2\pi}_0 f(x) dx= 0\), Wirtinger and Northcott showed that \[ \|f\|_{L_p[0,2\pi]}\leq C_\gamma(p)\|f^{(r)}\|_{L_p[0,2\pi]}. \] In this paper the author obtains that this inequality is valid for other operators, defined on various domains and spaces.
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On Wirtinger-type integral inequalities
Nonlinear functional analysis and applications, 2008In this paper some new Wirtinger-type integral inequalities involving many functions of many variables are established. Such inequalities generalize and improve some existing results of Agarwal and Sheng, and Cheung and Pečarić. The techniques used are algoritmic, and can be used to obtain other types of integral inequalities.
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Note on Wirtinger’s inequality
1997In this note we refine the following theorem due to W. Wirtinger: If f has period 2π and satisfies \( \int_0^{{2\pi }} {f(x)dx = 0} \), then $$ \int_0^{{2\pi }} {{f^2}(x)dx \leqslant {{\int_0^{{2\pi }} {f'} }^2}(x)dx} $$ with strict inequality unless f(x) = a cos(x) + b sin(x), (a, b ∈ ℝ).
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Wirtinger’s Inequality and Sampled-Data Control
2020Extensions of the discontinuous Lyapunov functional constructions proposed in Chap. 2 to sampled-data systems in the presence of input delay \(\eta \) lead to complicated conditions. Moreover, these conditions become conservative if \(\eta \) is not small.
Kun Liu, Emilia Fridman, Yuanqing Xia
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Euler's buckling formula and Wirtinger's inequality
International Journal of Mathematical Education in Science and Technology, 1983This article contains a discussion of Euler's buckling formula for a compressed elastic column. The most commonly used classroom derivations of this formula follow roughly the original arguments of Euler. For this reason the history of this problem is briefly reviewed.
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Discrete generalized Wirtinger's inequalities
Publicationes Mathematicae Debrecen, 2016openaire +1 more source
On the New Wirtinger Type Inequalities
2019The aim of this paper to establish a generalized and refinement of Wirtinger type inequality.
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