The random Kakutani fixed point theorem in random normed modules
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909826673541120 |
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| author | Tu, Qiang Mu, Xiaohuan Guo, Tiexin Yang, Guang Sun, Yuanyuan |
| author_facet | Tu, Qiang Mu, Xiaohuan Guo, Tiexin Yang, Guang Sun, Yuanyuan |
| contents | Based on the recently developed theory of random sequential compactness, we prove the random Kakutani fixed point theorem in random normed modules: if G is a random sequentially compact L0-convex subset of a random normed module, then every -stable Tc-upper semicontinuous mapping F:G to 2G such that F(x) is closed and L0-convex for each x in G, has a fixed point. This is the first fixed point theorem for set-valued mappings in random normed modules, providing a random generalization of the classical Kakutani fixed point theorem as well as a set-valued extension of the noncompact Schauder fixed point theorem established in Math. Ann. 391(3), 3863--3911 (2025). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15649 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The random Kakutani fixed point theorem in random normed modules Tu, Qiang Mu, Xiaohuan Guo, Tiexin Yang, Guang Sun, Yuanyuan Functional Analysis 46H25, 47H10, 46A22 Based on the recently developed theory of random sequential compactness, we prove the random Kakutani fixed point theorem in random normed modules: if G is a random sequentially compact L0-convex subset of a random normed module, then every -stable Tc-upper semicontinuous mapping F:G to 2G such that F(x) is closed and L0-convex for each x in G, has a fixed point. This is the first fixed point theorem for set-valued mappings in random normed modules, providing a random generalization of the classical Kakutani fixed point theorem as well as a set-valued extension of the noncompact Schauder fixed point theorem established in Math. Ann. 391(3), 3863--3911 (2025). |
| title | The random Kakutani fixed point theorem in random normed modules |
| topic | Functional Analysis 46H25, 47H10, 46A22 |
| url | https://arxiv.org/abs/2509.15649 |