Resolvent and Gronwall inequalities and fixed points of evolution operators
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916545854177280 |
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| author | Kalinin, Alexander |
| author_facet | Kalinin, Alexander |
| contents | We introduce kernels and resolvents on preordered sets and derive sharp resolvent inequalities that entail Gronwall inequalities for functions of several variables. In this way, we can prove a fixed point result for operators on topological spaces that extends Banach's fixed point theorem and allows for a wide range of applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20764 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Resolvent and Gronwall inequalities and fixed points of evolution operators Kalinin, Alexander Functional Analysis Classical Analysis and ODEs 26D10, 26A42, 26A33, 26B99, 47H10 We introduce kernels and resolvents on preordered sets and derive sharp resolvent inequalities that entail Gronwall inequalities for functions of several variables. In this way, we can prove a fixed point result for operators on topological spaces that extends Banach's fixed point theorem and allows for a wide range of applications. |
| title | Resolvent and Gronwall inequalities and fixed points of evolution operators |
| topic | Functional Analysis Classical Analysis and ODEs 26D10, 26A42, 26A33, 26B99, 47H10 |
| url | https://arxiv.org/abs/2412.20764 |