Comparing two integral means for absolutely continuous functions whose absolute value of the derivative are convex and applications

Hwang, Dah-Yan; Dragomir, Sever S

doi:10.1016/j.amc.2013.12.058

Cited by 6 publications

(10 citation statements)

References 17 publications

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“…The classical Jensen inequality [11][12][13][14][15][16][17][18] can be expressed as follows. Let the function f : I → R be a strictly convex function [12][13][14][15]. Then, for any X ∈ I n , we have the following discrete Jensen inequality…”

Section: Basic Concepts and Classical Resultsmentioning

confidence: 99%

“…Classical Jensen type inequalities and their applications were also investigated by many authors (see, e.g. [11][12][13][14][15][16][17][18]). In [15], the authors considered that comparing two integral means for absolutely continuous functions whose absolute value of the derivative are convex and displayed its applications.…”

Section: Introductionmentioning

confidence: 99%

“…[11][12][13][14][15][16][17][18]). In [15], the authors considered that comparing two integral means for absolutely continuous functions whose absolute value of the derivative are convex and displayed its applications. In [18] (see the proof of Lemma 2.10 in [18]), the authors displayed the applications of Jensen type inequalities in space science.…”

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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Section: Basic Concepts and Classical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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“…Recently, Hwang and Dragomir [18] proved the following result for absolutely continuous mapping whose first derivatives in absolute value is convex:…”

Section: Introductionmentioning

confidence: 99%

On two inequalities of Čebyšev

Alomari¹

2016

Preprint

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In this work, several sharp bounds for the Čebyšev functional involving various type of functions are proved. In particular, for the Čebyšev functional of two absolutely continuous functions whose first derivatives are both convex, convex and belong to Lp-spaces, convex and of bounded variation, convex and satisfies Lipschitz condition; new sharp bounds are presented. Other related results regarding two convex and concave functions are given.

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Relationships between integral averages for absolutely continuous functions whose derivative are GA-convex functions

Maden¹,

Turhan²,

Kadakal³

2017

AIP Conference Proceedings

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Comparing two integral means for absolutely continuous functions whose absolute value of the derivative are convex and applications

Cited by 6 publications

References 17 publications

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

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

On two inequalities of Čebyšev

Relationships between integral averages for absolutely continuous functions whose derivative are GA-convex functions

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