# Contraction mapping theorem

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

[Catalogue presentation and source-binding data](https://ocme.evemisslab.com/data/i18n/catalogue.en.json)



## [Contraction mapping theorem](https://ocme.evemisslab.com/en/atlas/atlas-contraction-mapping-theorem/)

A self-map on a nonempty complete metric space with one global contraction constant q<1 has a unique fixed point and convergent Picard iterates.

atlas-contraction-mapping-theorem · canonical_mko

[Contraction mapping theorem](https://ocme.evemisslab.com/en/mko/mko-contraction-mapping-theorem/)

## Prerequisite nodes


- [Orbits, fixed points and periodic points](https://ocme.evemisslab.com/en/atlas/atlas-orbit-fixed-periodic/)
- [Complete metric space](https://ocme.evemisslab.com/en/atlas/atlas-complete-metric-space/)
- [Convergence in a metric space](https://ocme.evemisslab.com/en/atlas/atlas-metric-convergence/)
- [Infinite series](https://ocme.evemisslab.com/en/atlas/atlas-infinite-series/)