Geodesic
On Some Relative Operator Entropies by Convex Inequalities
Journal of convex analysis, Tome 31 (2024) no. 3, pp. 983-998
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A considerable amount of literature on the theory of inequality is devoted to studying Jensen's and Young's inequality. This article presents a number of new inequalities involving the log-convex functions and the geometrically convex functions. As their consequences, we derive the refinements for Young's and Jensen's inequality. In addition, the operator Jensen's type inequality is also developed for conditioned two functions. Utilizing these new inequalities, we investigate the operator inequalities related to the relative operator entropy.
Classification : 26D15, 26A51, 39B62, 47A63, 47A64, 94A17
Mots-clés : Convexity, log-convex, geometrically convex, Jensen's inequality, relative operator entropy, operator inequality 
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     author = {S. Furuichi and H. R. Moradi and S. Dutta},
     title = {On {Some} {Relative} {Operator} {Entropies} by {Convex} {Inequalities}},
     journal = {Journal of convex analysis},
     pages = {983--998},
     year = {2024},
     volume = {31},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2024_31_3_JCA_2024_31_3_a12/}
}
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S. Furuichi; H. R. Moradi; S. Dutta. On Some Relative Operator Entropies by Convex Inequalities. Journal of convex analysis, Tome 31 (2024) no. 3, pp. 983-998. http://geodesic.mathdoc.fr/item/JCA_2024_31_3_JCA_2024_31_3_a12/