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| Main Author: | |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2106.13070 |
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| _version_ | 1866917624410013696 |
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| author | Pasteczka, Paweł |
| author_facet | Pasteczka, Paweł |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_13070 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | There is at most one continuous invariant mean Pasteczka, Paweł Classical Analysis and ODEs 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. |
| title | There is at most one continuous invariant mean |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2106.13070 |