On a Mercer like inequality involving generalized Csiszár f-divergences

DOI10.7153/mia-2021-24-08zbMath1471.26013OpenAlexW3134696511MaRDI QIDQ4991560

Marek Niezgoda

Publication date: 3 June 2021

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

Full work available at URL: https://doi.org/10.7153/mia-2021-24-08

zbMATH Keywords

convex functionMercer inequality\(p\)-majorizationcolumn row stochastic matrixgeneralized Csiszár \(f\)-divergencenonnegative entrywise matrix

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Inequalities for sums, series and integrals (26D15)

Cites Work

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• Extension of Jensen's inequality to affine combinations
• Vector joint majorization and generalization of Csiszár-Körner's inequality for \(f\)-divergence
• A generalization of Mercer's result on convex functions
• Parametric extensions of Shannon inequality and its reverse one in Hilbert space operators.
• Generalizations of Crooks and Lin's results on Jeffreys-Csiszár and Jensen-Csiszár \(f\)-divergences
• Generalized Shannon inequalities based on Tsallis relative operator entropy
• Shannon like inequalities for \(f\)-connections of positive linear maps and positive operators
• Generalizations of operator Shannon inequality based on Tsallis and Rényi relative entropies
• On Csiszár and Tsallis type f-divergences induced by superquadratic and convex functions
• Inequalities: theory of majorization and its applications

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