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## Banach Fixed-Point Theorem |

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z | overview |

If is a contraction of a non-empty closed set , i.e., if

- ,
- ,

More generally, the fixed point theorem holds in complete metric spaces. Since the proof neither requires translation invariance nor homogeneity of the norm, can be replaced by a general distance function .

**Example:**

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automatically generated 9/22/2016 |