On Csiszár and Tsallis type f-divergences induced by superquadratic and convex functions

DOI10.7153/mia-2018-21-31zbMath1384.26054OpenAlexW2793183768MaRDI QIDQ4634660

Marek Niezgoda, Paweł A. Kluza

Publication date: 11 April 2018

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

Full work available at URL: https://doi.org/10.7153/mia-2018-21-31

zbMATH Keywords

convex functionsuperquadratic functioncolumn stochastic matrixCsiszár \(f\)-divergenceTsallis \(f_{u}\)-divergence

Mathematics Subject Classification ID

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

Related Items (10)

On generalized Csiszár (f,g)-divergence with an application for p-majorization ⋮ On Jensen-Rényi and Jeffreys-Rényi type \(f\)-divergences induced by convex functions ⋮ Sherman's functional, its properties with applications for f-divergence measure ⋮ Hermite-Hadamard, Fejer and Sherman type inequalities for generalizations of superquadratic and convex functions ⋮ More accurate majorization inequalities obtained via superquadraticity and convexity with application to entropies ⋮ Converse to the Sherman inequality with applications ⋮ Equality cases of inequalities involving generalized Csiszár and Tsallis type f-divergences ⋮ Generalized Csiszár's f-divergence for Lipschitzian functions ⋮ On a Mercer like inequality involving generalized Csiszár f-divergences ⋮ Sherman's operator inequality

Cites Work

• On the Jensen functional and superquadraticity
• Vector joint majorization and generalization of Csiszár-Körner's inequality for \(f\)-divergence
• Improvement of Jensen-Steffensen's inequality for superquadratic functions
• Generalizations of Crooks and Lin's results on Jeffreys-Csiszár and Jensen-Csiszár \(f\)-divergences
• Possible generalization of Boltzmann-Gibbs statistics.
• Shannon like inequalities for \(f\)-connections of positive linear maps and positive operators
• Divergence measures based on the Shannon entropy
• Inequalities for H-invex functions with applications for uniformly convex and superquadratic functions
• Inequalities for relative operator entropies
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