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arXiv · 1501.02356

Explicit solutions of the invariance equation for means

Janusz Matkowski·Monika Nowicka·Alfred Witkowski
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Abstract

Extending the notion of projective means we first generalize an invariance identity related to the Carlson log given in a recent paper of P. Kahlig and J. Matkowski, 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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Janusz Matkowski, Monika Nowicka, Alfred Witkowski. 2015-01-10. Explicit solutions of the invariance equation for means. https://doi.org/10.1007/s00025-015-0525-4

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