Generalization of the Levinson inequality with applications to information theory

DOI10.1186/s13660-019-2186-4zbMath1499.26212OpenAlexW2969331856WikidataQ127315818 ScholiaQ127315818MaRDI QIDQ2067998

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

Publication date: 19 January 2022

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-019-2186-4

zbMATH Keywords

Levinson's inequalityinformation theory

Mathematics Subject Classification ID

Measures of information, entropy (94A17) Other analytical inequalities (26D20)

Related Items (14)

Difference equations related to majorization theorems via Montgomery identity and Green's functions with application to the Shannon entropy ⋮ Levinson type inequalities for higher order convex functions via Abel-Gontscharoff interpolation ⋮ Estimation of \(f\)-divergence and Shannon entropy by Levinson-type inequalities via new Green's functions and Lidstone polynomial ⋮ Estimation of entropies on time scales by Lidstone's interpolation using Csiszár-type functional ⋮ Estimation of divergence measures on time scales via Taylor's polynomial and Green's function with applications in \(q\)-calculus ⋮ Estimation of divergences on time scales via the Green function and Fink's identity ⋮ 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 ⋮ Retraction note to: ``Generalization of the Levinson inequality with applications to information theory ⋮ Majorization inequalities via Green functions and Fink's identity with applications to Shannon entropy ⋮ New entropic bounds on time scales via Hermite interpolating polynomial ⋮ Entropy results for Levinson-type inequalities via Green functions and Hermite interpolating polynomial

Cites Work

• Superadditivity of the Levinson functional and applications
• Zipf-Mandelbrot law, \(f\)-divergences and the Jensen-type interpolating inequalities
• Refinement of Jensen's inequality and estimation of \(f\)- and Rényi divergence via Montgomery identity
• Theory of statistical inference and information. Transl. from the Slovak by the author
• 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
• On Choosing and Bounding Probability Metrics
• Generalization of Jensen's inequality by Lidstone's polynomial and related results
• Some new Ostrowski-type bounds for the Čebyšev functional and applications
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