##  [Contraction Mapping Principle](/contraction-mapping-principle) 

  ##  [Contraction Mapping Principle](https://puremath.quantumdictionary.io/contraction-mapping-principle-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A theorem asserting that a self-map T on a complete metric space (X,d) that satisfies d(Tx,Ty) ≤ c d(x,y) for all x,y in X with some constant 0 ≤ c < 1 has a unique fixed point, and that iterative application of T converges to that fixed point.