On the Picard-Lindelöf Argument and the Banach-Caccioppoli Contraction Mapping Principle
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909978782072832 |
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| author | Bufetov, Alexander I. Zavolokin, Ilya I. |
| author_facet | Bufetov, Alexander I. Zavolokin, Ilya I. |
| contents | The aim of this note is to present the simple observation that a slight refinement of the Contraction Mapping Principle allows one to recover the precise convergence rate in the Picard-Lindelöf Theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24283 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Picard-Lindelöf Argument and the Banach-Caccioppoli Contraction Mapping Principle Bufetov, Alexander I. Zavolokin, Ilya I. Classical Analysis and ODEs Dynamical Systems Functional Analysis History and Overview 46N20, 34A05, 34-03 The aim of this note is to present the simple observation that a slight refinement of the Contraction Mapping Principle allows one to recover the precise convergence rate in the Picard-Lindelöf Theorem. |
| title | On the Picard-Lindelöf Argument and the Banach-Caccioppoli Contraction Mapping Principle |
| topic | Classical Analysis and ODEs Dynamical Systems Functional Analysis History and Overview 46N20, 34A05, 34-03 |
| url | https://arxiv.org/abs/2512.24283 |