Sherman's functional, its properties with applications for f-divergence measure

DOI10.7153/mia-2023-26-23zbMath1530.94012OpenAlexW4372059991MaRDI QIDQ6180065

Josip E. Pečarić, Đilda Pečarić, Slavica Ivelić Bradanović

Publication date: 18 January 2024

Published in: Mathematical Inequalities & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7153/mia-2023-26-23

zbMATH Keywords

Shannon's entropyJensen's functionalZipf-Mandelbrot lawCsiszár \(f\)-divergenceSherman's inequality

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Measures of information, entropy (94A17) Stochastic matrices (15B51)

Cites Work

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• Relative convexity and its applications
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• Remarks on convex functions and separable sequences
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• Generalizations of Sherman's inequality by Hermite's interpolating polynomial
• Remarks on Sherman like inequalities for (α,β)-convex functions
• Bounds for the normalised Jensen functional
• On Csiszár and Tsallis type f-divergences induced by superquadratic and convex functions
• Sherman's operator inequality
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• Sherman's inequality and its converse for strongly convex functions with applications to generalized f-divergences
• Converse to the Sherman inequality with applications
• On Information and Sufficiency
• On a Theorem of Hardy, Littlewood, Polya, and Blackwell

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