Chebyshev type inequalities involving permanents and their applications

The Hardy matrix H n (x, α), the Hardy function per H n (x, α) and the generalized Vandermonde determinant det H n (x, α) are defined in this paper. By means of algebra and analysis theories together with proper hypotheses, we establish the following Minkowski-type inequality involving Hardy function:As applications, our inequality is used to estimate the lower bounds of the increment of a symmetric function. MSC: 26D15; 15A15

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“…China. 2 Department of Mathematics and Computer Science, Longyan University, Longyan, Fujian 364012, P.R. China.…”

Section: Competing Interestsmentioning

confidence: 99%

Minkowski-type inequalities involving Hardy function and symmetric functions

Wen

Han

2014

J Inequal Appl

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“…Classical Chebyshev type inequalities and their applications were investigated by many authors (see, e.g. [1][2][3][4][5][6][7][8][9][10]). In [1], the authors considered some new bivariate Chebyshev-Grüss-type inequalities via discrete oscillations and to apply them to different tensor products of linear positive.…”

Section: Introductionmentioning

confidence: 99%

“…In [1], the authors considered some new bivariate Chebyshev-Grüss-type inequalities via discrete oscillations and to apply them to different tensor products of linear positive. In [2], the authors established Chebyshev type inequalities involving the permanents of matrix as follows:…”

Section: Introductionmentioning

confidence: 99%

“…The research tools of the paper include the functional analysis, discrete mathematics, probability [17,19,20,[22][23][24][25][26][27], convex geometry [28], linear algebra [2], inequality and the mean value [15,16,18,27,[29][30][31][32][33][34] theories, especially the mean value theory. The research methods of the paper are based on the mathematical induction [2,17,18,32], reorder method [2] and the dimension reduction method [32].…”

Section: Introductionmentioning

confidence: 99%

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Chebyshev-Jensen-type inequalities and their applications in probability theory with surround system

Wen

Han

Yuan

2023

Preprint

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This paper will establish Chebyshev-Jensen-type inequalities which involving the Chebyshev products as follows:\[\langle X^{1}, X^{2}, \ldots, X^{m}\rangle_{\chi}\geq \left[ X^{1}, X^{2}, \ldots, X^{m}\right]_{\chi}\geq \chi\left( \overline{X^{1}}, \overline{X^{2}}, \ldots, \overline{X^{m}}\right)\]and\[\langle f_{1}, f_{2}, \ldots, f_{m}\rangle_{\chi}\geq \left[f_{1}, f_{2}, \ldots,f_{m}\right]_{\chi}\geq \chi\left( \overline{f_{1}}, \overline{f_{2}}, \ldots, \overline{f_{m}}\right),\]as well as display their applications in probability theory and surround system, especially, the observation angles inequalities are obtained as follows:\[1\geq \frac{1}{n}\sum_{i=1}^{n}P\left(R_{i}\right)\geq \frac{1}{n^{m}}\sum_{1\leq i_{1},\ldots,i_{m}\leq n}P(R_{i_{1},\ldots,i_{m}})\geq\left(\frac{2}{n}\right)^{m+|\alpha|}.\]The research methods of the paper are based on the mathematical induction, reorder method and the dimension reduction method. 2010 MSC: 26D15, 26E60, 51K05, 52A40

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“…We close our investigation by remarking that results similar to Theorem 1 can be established if R m is replaced by more general linear spaces endowed with appropriate algebraic operations and compatible norms, and many methods and techniques related to the mathematical inequalities used in this article can be found in [1][2][3][5][6][7][8][9].…”

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confidence: 99%

Closed balls for interpolating quasi-polynomials

Wen

Cheng

2011

Comput. Appl. Math.

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Abstract. The classic interpolation problem asks for polynomials to fit a set of given data.In this paper, quasi-polynomials are considered as interpolating functions passing through a set of spatial points. Existence and uniqueness is obtained by means of generalized Vandermonde determinants. By means of several estimates related to these determinants, we are also able to find closed balls for any given centers that enclose the approximating curves. By choosing proper centers based on the observed spatial points, these balls may lead us to applications such as satellite tracking and control.Mathematical subject classification: 41A05.

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Chebyshev type inequalities involving permanents and their applications

Cited by 25 publications

References 2 publications

Minkowski-type inequalities involving Hardy function and symmetric functions

Minkowski-type inequalities involving Hardy function and symmetric functions

Chebyshev-Jensen-type inequalities and their applications in probability theory with surround system

Closed balls for interpolating quasi-polynomials

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