Journal of Convex Analysis 31 (2024), No. 3, 983--998
Copyright Heldermann Verlag 2024
On Some Relative Operator Entropies by Convex Inequalities
Shigeru Furuichi
Dept. of Information Science, College of Humanities and Sciences, Nihon University, Tokyo, Japan
furuichi.shigeru@nihon-u.ac.jp
Hamid Reza Moradi
Dept. of Mathematics, Payame Noor University, Tehran, Iran
hrmoradi@mshdiau.ac.ir
Supriyo Dutta
Dept. of Mathematics, National Institute of Technology Agartala, Tripura, India
dosupriyo@gmail.com
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.
Keywords: Convexity, log-convex, geometrically convex, Jensen's inequality, relative operator entropy, operator inequality.
MSC: 26D15, 26A51, 39B62, 47A63, 47A64, 94A17.
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