##  [Banach Fixed-Point Theorem](/banach-fixed-point-theorem) 

  ##  [Banach Fixed-Point Theorem](https://natural.quantumdictionary.io/banach-fixed-point-theorem-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

In a complete metric space, any mapping that is a contraction (reduces distances by a uniform factor strictly less than one) has a unique fixed point, and iterating the map from any initial point converges geometrically to that fixed point.