# Kakutani fixed-point theorem

> theorem that a function f: S→Pow(S) on a compact nonempty convex subset S⊂ℝⁿ, whose graph is closed and whose image f(x) is nonempty and convex for all x∈S, has a fixed point

**Wikidata**: [Q518524](https://www.wikidata.org/wiki/Q518524)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Kakutani_fixed-point_theorem)  
**Source**: https://4ort.xyz/entity/kakutani-fixed-point-theorem


## References

1. Freebase Data Dumps. 2013
2. [OpenAlex](https://docs.openalex.org/download-snapshot/snapshot-data-format)