About the sharpness of the Jensen inequality

DOI10.1186/s13660-018-1923-4zbMath1498.26067OpenAlexW2903768695WikidataQ60304327 ScholiaQ60304327MaRDI QIDQ2061474

Mirna Rodić, 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/s13660-018-1923-4

zbMATH Keywords

entropyGreen functionJensen inequality\(f\)-divergenceZipf-Mandelbrot law

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) Inequalities for sums, series and integrals (26D15) Measures of information, entropy (94A17)

Related Items (4)

Bounds for the Jensen gap in terms of power means with applications ⋮ New converses of Jensen inequality via Green functions with applications ⋮ On a Jensen-type inequality for generalized f-divergences and Zipf-Mandelbrot law ⋮ A new bound for the Jensen gap pertaining twice differentiable functions with applications

Cites Work

• Zipf-Mandelbrot law, \(f\)-divergences and the Jensen-type interpolating inequalities
• Theory of statistical inference and information. Transl. from the Slovak by the author
• How sharp is the Jensen inequality?
• Estimations of \(f\)- and Rényi divergences by using a cyclic refinement of the Jensen's inequality
• Inequalities of the Jensen and Edmundson-Lah-Ribarič type for 3-convex functions with applications
• Beyond the Zipf-Mandelbrot law in quantitative linguistics
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