The Hasegawa-Petz mean: Properties and inequalities

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:391

Article

Besenyei, Adam

关键词: Hasegawa-Petz mean;    Monotonicity;    Concavity;    Comparison;    Stolarsky mean;    Operator monotone function;   

DOI  :  10.1016/j.jmaa.2012.02.055

来源: Elsevier

【 摘 要 】

We study a family of means introduced by H. Hasegawa and D. Petz (1996) [13]. 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. (C) 2012 Elsevier Inc. All rights reserved.

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