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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.10002 |
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| _version_ | 1866914464889044992 |
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| author | Lakzian, Sajjad |
| author_facet | Lakzian, Sajjad |
| contents | We present a generalization of the inverse mapping theorem, where variations of a weaker non-expansiveness property (referred to as property ${\sf A}$) replace the key $\mathsf{C}^1$ condition. We also obtain inverse mapping theorems that can be applied to non-smooth maps. Also as a by-product of the generalized inverse mapping theorem, we prove generalizations of the implicit function theorem and existence and uniqueness theorem of abstract PDE systems as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10002 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A generalization of the inverse mapping theorem in infinite dimensions Lakzian, Sajjad Functional Analysis Analysis of PDEs Differential Geometry 46Bxx, 46Txx We present a generalization of the inverse mapping theorem, where variations of a weaker non-expansiveness property (referred to as property ${\sf A}$) replace the key $\mathsf{C}^1$ condition. We also obtain inverse mapping theorems that can be applied to non-smooth maps. Also as a by-product of the generalized inverse mapping theorem, we prove generalizations of the implicit function theorem and existence and uniqueness theorem of abstract PDE systems as well. |
| title | A generalization of the inverse mapping theorem in infinite dimensions |
| topic | Functional Analysis Analysis of PDEs Differential Geometry 46Bxx, 46Txx |
| url | https://arxiv.org/abs/2604.10002 |