A General Fixed-Point Theorem for Correspondences
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914175620481024 |
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| author | Vohra, Ranjit |
| author_facet | Vohra, Ranjit |
| contents | A new local condition on correspondences called the "weak local connectedness property" (WLCP) is introduced. Working in ZFC, it is shown in our main theorem that - under mild restrictions - any correspondence from a connected subset X of a real TVS to itself will have a fixed point if the WLCP holds at each point of the domain. Since the WLCP generalizes several well - known conditions on correspondences, it is utilized in this paper to gather together a sampling of several disparate fixed-point and related results that are special cases of our main theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15909 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A General Fixed-Point Theorem for Correspondences Vohra, Ranjit General Mathematics A new local condition on correspondences called the "weak local connectedness property" (WLCP) is introduced. Working in ZFC, it is shown in our main theorem that - under mild restrictions - any correspondence from a connected subset X of a real TVS to itself will have a fixed point if the WLCP holds at each point of the domain. Since the WLCP generalizes several well - known conditions on correspondences, it is utilized in this paper to gather together a sampling of several disparate fixed-point and related results that are special cases of our main theorem. |
| title | A General Fixed-Point Theorem for Correspondences |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2510.15909 |