Estimation of f-divergence and Shannon entropy by Levinson type inequalities for higher order convex functions via Taylor polynomial

Adeel, Muhammad; Khan, Khuram Ali; Pec̆arić, Ðilda; Pečarić, Josip

doi:10.22436/jmcs.021.04.05

Cited by 14 publications

(19 citation statements)

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“…We further make con-nection of majorization with information theory and discuss our generalized majorization inequality in terms of divergences and entropies. The results we obtain in this paper are closely related to the contents given in [1][2][3][4][5]. Moreover, some related results with the present topic can also be found in [10,11,27,41,42].…”

Section: Introductionsupporting

confidence: 84%

Difference equations related to majorization theorems via Montgomery identity and Green’s functions with application to the Shannon entropy

et al. 2020

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In this paper we give generalized results of a majorization inequality by using extension of the Montgomery identity and newly defined Green's functions (Mehmood et al. in J. Inequal. Appl. 2017(1):108, 2017). We obtain a generalized majorization theorem for the class of n-convex functions. We use Csiszár f-divergence and generalized majorization-type inequalities to obtain new generalized results. We further discuss our obtained generalized results in terms of the Shannon entropy and the Kullback-Leibler distance.

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Section: Introductionsupporting

confidence: 84%

Difference equations related to majorization theorems via Montgomery identity and Green’s functions with application to the Shannon entropy

et al. 2020

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“…We further make connection of majorization with information theory and discuss our generalized majorization inequality in terms of divergences and entropies. The results we obtain in this paper are closely related to the contents of [1][2][3][4][5]. Moreover, some results related to the present topic can also be found in [19].…”

Section: Introductionsupporting

confidence: 76%

“…, k). Then conditions (45) and (46) imply conditions (4) and (5). So using these substitutions in (37), we get (47).…”

Section: Csiszár F-divergence For Majorizationmentioning

confidence: 90%

Majorization inequalities via Green functions and Fink’s identity with applications to Shannon entropy

et al. 2020

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This paper is devoted to obtain generalized results related to majorization-type inequalities by using well-known Fink's identity and new types of Green functions, introduced by Mehmood et al. (J. Inequal. Appl. 2017:108, 2017). We give a generalized majorization theorem for the class of n-convex functions. We utilize the Csiszár f-divergence and generalized majorization-type inequalities in providing the corresponding generalizations. As an application, we present the obtained results in terms of Shannon entropy and Kullback-Leibler distance.

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“…The function ΨðxÞ = x 1/p is both convex and 4-convex for x ≥ 0 with p ∈ ð0, 1Þ such that 1/p ∉ ð2, 3Þ. Therefore, inequality (21) can easily be acquired by putting ΨðxÞ = x 1/p , p i = γ i q , and x i = γ i −q ζ p i in (7). Now, we recall the definition of power mean.…”

Section: Applications For Classical Inequalitiesmentioning

confidence: 99%

“…The Jensen inequality has multitudinous applications in Mathematics [7][8][9][10][11], Statistics [12], Economics [13] and Information Theory [14], etc. The most interesting and attractive applications of this inequality is that it generalized the classical convexity.…”

Section: Introductionmentioning

confidence: 99%

Some Improvements of Jensen’s Inequality via 4-Convexity and Applications

Ullah

Khan

Saeed

et al. 2022

Journal of Function Spaces

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The intention of this note is to investigate some new important estimates for the Jensen gap while utilizing a 4-convex function. We use the Jensen inequality and definition of convex function in order to achieve the required estimates for the Jensen gap. We acquire new improvements of the Hölder and Hermite–Hadamard inequalities with the help of the main results. We discuss some interesting relations for quasi-arithmetic and power means as consequences of main results. At last, we give the applications of our main inequalities in the information theory. The approach and techniques used in the present note may simulate more research in this field.

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Estimation of f-divergence and Shannon entropy by Levinson type inequalities for higher order convex functions via Taylor polynomial

Cited by 14 publications

References 0 publications

Difference equations related to majorization theorems via Montgomery identity and Green’s functions with application to the Shannon entropy

Difference equations related to majorization theorems via Montgomery identity and Green’s functions with application to the Shannon entropy

Majorization inequalities via Green functions and Fink’s identity with applications to Shannon entropy

Some Improvements of Jensen’s Inequality via 4-Convexity and Applications

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