Estimations of f- and Rényi Divergences by Using a Cyclic Refinement of the Jensen’s Inequality

Horváth, László; Pec̆arić, Ðilda; Pečarić, Josip

doi:10.1007/s40840-017-0526-4

Cited by 57 publications

(60 citation statements)

References 8 publications

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“…where G k (·, s) are defined by (10) and (12) (19) holds. Then we can represent the function f in the form (9). Now by means of some simple calculations we can write…”

Section: Resultsmentioning

confidence: 99%

Generalization of the Levinson inequality with applications to information theory

et al. 2019

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In the presented paper, Levinson's inequality for the 3-convex function is generalized by using two Green functions.Čebyšev-, Grüss-and Ostrowski-type new bounds are found for the functionals involving data points of two types. Moreover, the main results are applied to information theory via the f -divergence, the Rényi divergence, the Rényi entropy, the Shannon entropy and the Zipf-Mandelbrot law.

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“…where G k (·, s) are defined by (10) and (12) (19) holds. Then we can represent the function f in the form (9). Now by means of some simple calculations we can write…”

Section: Resultsmentioning

confidence: 99%

Generalization of the Levinson inequality with applications to information theory

et al. 2019

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“…In [17] L. Horváth et al introduced some new functionals based on the f -divergence functionals, and obtained some estimates for the new functionals. They obtained f -divergence and Rényi divergence by applying a cyclic refinement of Jensen's inequality.…”

Section: Introduction and Preliminary Resultsmentioning

confidence: 99%

Estimation of Different Entropies via Taylor One Point and Taylor Two Points Interpolations Using Jensen Type Functionals

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Khan

Pec̆arić

et al. 2019

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“…(ii) It is a special case of (i). [16]) The Kullback-Leibler divergence between the positive probability distribution r = (r 1 , . .…”

Section: Inequalities For Shannon Entropymentioning

confidence: 99%

“…Under the assumption of Theorem 4.2 (ii), consider the following functionals: 16 ( f ) = A [8] m,r − D 1 (r, q), r = 1, . .…”

Section: Shannon Entropy Zipf-mandelbrot Law and Hybrid Zipf-mandelmentioning

confidence: 99%

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Estimation of different entropies via Lidstone polynomial using Jensen-type functionals

et al. 2020

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In this work, some new functional of Jensen-type inequalities are constructed using Shannon entropy, f -divergence, and Rényi divergence, and some estimates are obtained for these new functionals. Also using the Zipf-Mandelbrot law and hybrid Zipf-Mandelbrot law, we investigate some bounds for these new functionals. Furthermore, we generalize these new functionals for m-convex function using Lidstone polynomial.Mathematics Subject Classification 94Axx · 39-XX · 41A58

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Estimations of f- and Rényi Divergences by Using a Cyclic Refinement of the Jensen’s Inequality

Cited by 57 publications

References 8 publications

Generalization of the Levinson inequality with applications to information theory

Generalization of the Levinson inequality with applications to information theory

Estimation of Different Entropies via Taylor One Point and Taylor Two Points Interpolations Using Jensen Type Functionals

Estimation of different entropies via Lidstone polynomial using Jensen-type functionals

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