Refinement of Jensen's inequality and estimation of \(f\)- and Rényi divergence via Montgomery identity

DOI10.1186/s13660-018-1902-9zbMath1498.26052OpenAlexW2901785719WikidataQ59796016 ScholiaQ59796016MaRDI QIDQ824889

Tasadduq Niaz, Khuram Ali Khan, Đilda Pečarić, Josip E. Pečarić

Publication date: 15 December 2021

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

Full work available at URL: https://doi.org/10.1186/s13660-018-1902-9

zbMATH Keywords

entropyJensen inequalityRényi divergenceMontgomery identity\(f\)-divergence\(m\)-convex function

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Measures of information, entropy (94A17) Convexity of real functions in one variable, generalizations (26A51) Inequalities involving other types of functions (26D07)

Related Items (16)

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 ⋮ Unnamed Item ⋮ Extension of Montgomery identity via Taylor polynomial on time scales ⋮ Unnamed Item ⋮ New improvements of Jensen's type inequalities via 4-convex functions with applications ⋮ Estimation of different entropies via Hermite interpolating polynomial using Jensen-type functionals ⋮ Levinson-type inequalities via new Green functions and Montgomery identity ⋮ RETRACTED ARTICLE: Generalization of the Levinson inequality with applications to information theory ⋮ Generalization of the Levinson inequality with applications to information theory ⋮ Estimation of f-divergence and Shannon entropy by using Levinson type inequalities for higher order convex functions via Hermite interpolating polynomial ⋮ New entropic bounds on time scales via Hermite interpolating polynomial ⋮ A new bound for the Jensen gap pertaining twice differentiable functions with applications ⋮ Entropy results for Levinson-type inequalities via Green functions and Hermite interpolating polynomial

Cites Work

• A method to refine the discrete Jensen's inequality for convex and mid-convex functions
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• Convex functions, partial orderings, and statistical applications
• New generalizations of Popoviciu type inequalities via new Green functions and Fink's identity
• Popoviciu type inequalities via Hermite's polynomial
• A refinement of the discrete Jensen's inequality
• On Information and Sufficiency
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