Explicit Solutions of the Invariance Equation for Means

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• 作者：Janusz Matkowski ; Monika Nowicka ; Alfred Witkowski
• 关键词：Invariant means ; homogeneous means
• 刊名：Results in Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：71
• 期：1-2
• 页码：397-410
• 全文大小：488KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1420-9012
• 卷排序：71

文摘

Extending the notion of projective means we first generalize an invariance identity related to the Carlson log given in Kahlig and Matkowski (Math Inequal Appl 18(3):1143–1150, 2015), and then, more generally, given a bivariate symmetric, homogeneous and monotone mean M, we give explicit formula for a rich family of pairs of M-complementary means. We prove that this method cannot be extended for higher dimension. Some examples are given and two open questions are proposed.