Periodic points of mappings contracting total pairwise distance
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913764683546624 |
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| author | Petrov, Evgeniy |
| author_facet | Petrov, Evgeniy |
| contents | We consider a new type of mappings in metric spaces so-called mappings contracting total pairwise distance on $n$ points. It is shown that such mappings are continuous. A theorem on the existence of periodic points for such mappings is proved and the classical Banach fixed-point theorem is obtained like a simple corollary as well as the fixed-point theorem for mappings contracting perimeters of triangles. Examples of mappings contracting total pairwise distance on $n$ points and having different properties are constructed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02536 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Periodic points of mappings contracting total pairwise distance Petrov, Evgeniy General Topology Primary 47H09, Secondary 47H10 We consider a new type of mappings in metric spaces so-called mappings contracting total pairwise distance on $n$ points. It is shown that such mappings are continuous. A theorem on the existence of periodic points for such mappings is proved and the classical Banach fixed-point theorem is obtained like a simple corollary as well as the fixed-point theorem for mappings contracting perimeters of triangles. Examples of mappings contracting total pairwise distance on $n$ points and having different properties are constructed. |
| title | Periodic points of mappings contracting total pairwise distance |
| topic | General Topology Primary 47H09, Secondary 47H10 |
| url | https://arxiv.org/abs/2402.02536 |