# 壓縮映射定理

[目錄呈現與來源綁定資料](https://ocme.evemisslab.com/data/i18n/catalogue.en.json)



## [壓縮映射定理](https://ocme.evemisslab.com/zh-Hant/atlas/atlas-contraction-mapping-theorem/)

非空完備度量空間上的self-map若以固定q<1壓縮所有距離，則有唯一fixed point且Picard orbit收斂。

atlas-contraction-mapping-theorem · canonical_mko

[壓縮映射定理](https://ocme.evemisslab.com/zh-Hant/mko/mko-contraction-mapping-theorem/)

## 前置節點


- [軌道、固定點與週期點](https://ocme.evemisslab.com/zh-Hant/atlas/atlas-orbit-fixed-periodic/)
- [完備度量空間](https://ocme.evemisslab.com/zh-Hant/atlas/atlas-complete-metric-space/)
- [度量空間中的收斂](https://ocme.evemisslab.com/zh-Hant/atlas/atlas-metric-convergence/)
- [無窮級數](https://ocme.evemisslab.com/zh-Hant/atlas/atlas-infinite-series/)