Abstract The purpose of this paper is to introduce the logarithmic mean of two convex functionals that extends the logarithmic mean of two positive operators. Some inequalities involving this functional mean are discussed as well. The operator versions of the functional theoretical results obtained here are immediately deduced without referring to the theory of operator means.

中文翻译：

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两个凸函数的对数平均值

摘要 本文的目的是介绍扩展两个正算子的对数均值的两个凸函数的对数均值。还讨论了涉及此功能均值的一些不等式。此处获得的函数理论结果的算子版本是立即推导出来的，无需参考算子均值理论。