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arXiv · 2106.13070

There is at most one continuous invariant mean

Paweł Pasteczka
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Abstract

We show that, for a (not necessarily continuous) weakly contractive mean-type mapping $\mathbf{M} \colon I^p\to I^p$ (where $I$ is an interval and $p \in \mathbb{N}$), the functional equation $K \circ \mathbf{M}=K$ has at most one solution in the family of continuous means $K \colon I^p \to I$. Some general approach to the latter equation is also given.

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Paweł Pasteczka. 2021-06-24. There is at most one continuous invariant mean. https://doi.org/10.1007/s00010-022-00870-w

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