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<p>In-betweenness property with given order relation is a natural condition for a two-variable mean. We study this property for the quasi-arithmetic mean, log-Euclidean mean, and Rényi mean. Especially, we show the monotonicity of quasi-arithmetic mean on both variables and parameters with respect to the chaotic order. Finally, we provide the Schatten <i>p</i>-norm inequalities of Heinz mean types with the Rényi mean, spectral geometric mean and Wasserstein mean.</p>

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In-betweenness and Heinz mean inequalities

  • 期刊论文

  • 发表日期：

    2025年5月2日

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  • Raluca Dumitru,
  • Jose A. Franco,
  • Sejong Kim

摘要

In-betweenness property with given order relation is a natural condition for a two-variable mean. We study this property for the quasi-arithmetic mean, log-Euclidean mean, and Rényi mean. Especially, we show the monotonicity of quasi-arithmetic mean on both variables and parameters with respect to the chaotic order. Finally, we provide the Schatten p-norm inequalities of Heinz mean types with the Rényi mean, spectral geometric mean and Wasserstein mean.