Revision #1689 → #2427 · back to history
modifiedStrict contraction without uniform constant: T(x)=x+1/x158881f71cbd
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| anchor.section | Statement | — |
| anchor.snippet | is in general not enough to ensure the existence of a fixed point | — |
| provenance | ai | ai-moderated |
modifiedApplication: Picard–Lindelöf theorem462afb908a2c
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| mathlib.module | Mathlib.Analysis.ODE.PicardLindelof | Mathlib.Analysis.ODE.ExistUnique |
| note | Mathlib's Picard–Lindelöf is proved exactly via Banach's theorem applied to the integral (Picard) operator; see `ODE.picard` and `FunSpace.exists_isFixedPt_next` which use `ContractingWith.isFixedPt_fixedPoint_iterate`. | Mathlib's Picard–Lindelöf existence-uniqueness statement, proved via Banach's theorem applied to the Picard integral operator (with `ContractingWith.isFixedPt_fixedPoint_iterate` as the key step). |
addedFixed point98696f6eb144
addedComplete metric spacecdb960f0f40a
addedProof: Picard iterates form a Cauchy sequenceb366825b8271