Estimation of \(f\)-divergence and Shannon entropy by Levinson-type inequalities via new Green's functions and Lidstone polynomial

DOI10.1186/s13662-020-2501-xzbMath1487.94058OpenAlexW3028717023WikidataQ126355873 ScholiaQ126355873MaRDI QIDQ2144030

Muhammad Adeel, Đilda Pečarić, Khuram Ali Khan, Josip E. Pečarić

Publication date: 1 June 2022

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-020-2501-x

zbMATH Keywords

Green functionsinformation theoryLevinson inequalityLidstone interpolating polynomial

Mathematics Subject Classification ID

Measures of information, entropy (94A17) Information theory (general) (94A15) Other analytical inequalities (26D20)

Related Items (7)

Difference equations related to majorization theorems via Montgomery identity and Green's functions with application to the Shannon entropy ⋮ Estimation of entropies on time scales by Lidstone's interpolation using Csiszár-type functional ⋮ Generalizations of Levinson type inequalities via new Green functions with applications to information theory ⋮ Unnamed Item ⋮ Levinson-type inequalities via new Green functions and Montgomery identity ⋮ Estimation of f-divergence and Shannon entropy by using Levinson type inequalities for higher order convex functions via Hermite interpolating polynomial ⋮ Majorization inequalities via Green functions and Fink's identity with applications to Shannon entropy

Cites Work

• Refinement of Jensen's inequality and estimation of \(f\)- and Rényi divergence via Montgomery identity
• Convex functions, partial orderings, and statistical applications
• Theory of statistical inference and information. Transl. from the Slovak by the author
• Generalization of the Levinson inequality with applications to information theory
• Levinson type inequalities for higher order convex functions via Abel-Gontscharoff interpolation
• Generalization of an inequality of Ky Fan
• Estimations of \(f\)- and Rényi divergences by using a cyclic refinement of the Jensen's inequality
• $f$ -Divergence Inequalities
• Generalized Levinson's inequality and exponential convexity
• Linear operators inequality for $n$-convex functions at a point
• On Choosing and Bounding Probability Metrics
• Generalization of Jensen's inequality by Lidstone's polynomial and related results
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