---
tag: 012PBA0FMD
kind: concept
name: Hölder continuity
aliases: [holder-condition, holder-continuous-map]
msc: [26A16]
sources:
  - url: https://en.wikipedia.org/wiki/H%C3%B6lder_condition
    locator: lead section
same_as:
  wikidata: Q91259930
  wikipedia: Hölder condition
---

## Summary

A map between metric spaces is Hölder continuous with exponent $\alpha$ when $d(f(x), f(y)) \le C \, d(x, y)^\alpha$ for some constant $C$ and all $x, y$.
For $\alpha = 1$ this is the Lipschitz condition.