Construction of graph-directed invariant sets of weak contractions on semi-metric spaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915893840183296 |
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| author | Okamura, Kazuki |
| author_facet | Okamura, Kazuki |
| contents | We present a construction of graph-directed invariant sets of weak contractions in the sense of Matkowski-Rus on semi-metric spaces. We follow the approach by Bessenyei and Pénzes, which applies the Kuratowski noncompactness measure without relying on Blascke's completeness theorem. We also establish a relationship between this approach and a generalized de Rham's functional equation indexed by a finite directed graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23423 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Construction of graph-directed invariant sets of weak contractions on semi-metric spaces Okamura, Kazuki Metric Geometry Classical Analysis and ODEs Functional Analysis 39B12, 39B72, 47H09, 47H10, 28A80 We present a construction of graph-directed invariant sets of weak contractions in the sense of Matkowski-Rus on semi-metric spaces. We follow the approach by Bessenyei and Pénzes, which applies the Kuratowski noncompactness measure without relying on Blascke's completeness theorem. We also establish a relationship between this approach and a generalized de Rham's functional equation indexed by a finite directed graph. |
| title | Construction of graph-directed invariant sets of weak contractions on semi-metric spaces |
| topic | Metric Geometry Classical Analysis and ODEs Functional Analysis 39B12, 39B72, 47H09, 47H10, 28A80 |
| url | https://arxiv.org/abs/2503.23423 |