Abstract
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.
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Matkowski, J., Nowicka, M. & Witkowski, A. Explicit Solutions of the Invariance Equation for Means. Results Math 71, 397–410 (2017). https://doi.org/10.1007/s00025-015-0525-4
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DOI: https://doi.org/10.1007/s00025-015-0525-4