The Hasegawa-Petz mean: Properties and inequalities

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• 作者：Á ; dá ; m Besenyei ^{badam@cs.elte.hu}
• 关键词：Hasegawa&ndash ; Petz mean ; Monotonicity ; Concavity ; Comparison ; Stolarsky mean ; Operator monotone function
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2012
• 期刊代码：76_0022247x
• 类别：mt
• 出版时间：15 July, 2012
• 卷：391
• 期：2
• 页码：441-450
• 文件大小：170 K

摘要

We study a family of means introduced by H. Hasegawa and D. Petz (1996) . Properties with respect to the parameter, such as monotonicity and logarithmic concavity, further, monotonicity and concavity in the mean variables are shown. Besides, the comparison between the Hasegawa-Petz mean and the geometric mean is completely solved. The connection to earlier results on operator monotonicity and some applications are also discussed.