Theorems · Theorem · general topology
ContractingWith.apriori_dist_iterate_fixedPoint_le
∀ {α : Type u_1} [inst : MetricSpace α] {K : NNReal} {f : α → α} (hf : ContractingWith K f) [inst_1 : Nonempty α]
[inst_2 : CompleteSpace α] (x : α) (n : ℕ),
dist (f^[n] x) (ContractingWith.fixedPoint f hf) ≤ dist x (f x) * ↑K ^ n / (1 - ↑K)- Defined in
- Mathlib.Topology.MetricSpace.Contracting
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- NNRealstatement and proof · cited by 4,310
- CompleteSpacestatement and proof · cited by 2,532
- LT.lt.leproof · cited by 2,189
- MetricSpacestatement and proof · cited by 1,684
- Dist.diststatement · cited by 1,539
- NNReal.toRealstatement · cited by 1,260
- Nat.iteratestatement · cited by 740
- div_le_div_of_nonneg_rightproof · cited by 77
- ContractingWithstatement and proof · cited by 39
- ContractingWith.fixedPointstatement · cited by 9
- ContractingWith.toLipschitzWithproof · cited by 4
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.