Kakutani fixed-point theorem

Summary

Kakutani fixed-point theorem is a fixed-point theorem^[1]. It draws 122 Wikipedia views per month (fixed_point_theorem category, ranking #3 of 14).^[2]

Key Facts

• Kakutani fixed-point theorem is credited with the discovery of Shizuo Kakutani^[3].
• Kakutani fixed-point theorem's instance of is recorded as fixed-point theorem^[4].
• Shizuo Kakutani is named after Kakutani fixed-point theorem^[5].
• Kakutani fixed-point theorem's subclass of is recorded as fixed-point theorems in infinite-dimensional spaces^[6].
• Kakutani fixed-point theorem's time of discovery or invention is recorded as +1938-00-00T00:00:00Z^[7].
• Kakutani fixed-point theorem's Freebase ID is recorded as /m/07vxx7^[8].
• Kakutani fixed-point theorem's defining formula is recorded as \begin{aligned}&f\colon S\to\operatorname{Pow}(S)\&S\subset\mathbb R^n\&S\ne\varnothing\land\operatorname{conv}(S)=\operatorname{cl}(S)=S\land\sup_{x\in S}|s|<\infty\land{(x,y)\colon y\in f(x)}=\operatorname{cl}({(x,y)\colon y\in f(x)})\land \left(\forall x\in S\colon(f(x)\ne\varnothing \land\operatorname{conv}(f(x))=f(x))\right)\implies\exists s\in S\colon s\in\phi(s)\end{aligned}^[9].
• Kakutani fixed-point theorem's studied by is recorded as convex geometry^[10].
• Kakutani fixed-point theorem's studied by is recorded as topology^[11].
• Kakutani fixed-point theorem's JSTOR topic ID is recorded as kakutani-theorem^[12].
• Kakutani fixed-point theorem's maintained by WikiProject is recorded as WikiProject Mathematics^[13].
• Kakutani fixed-point theorem's Microsoft Academic ID is recorded as 134618013^[14].
• Kakutani fixed-point theorem's generalization of is recorded as Brouwer fixed-point theorem^[15].
• Kakutani fixed-point theorem's OpenAlex ID is recorded as C134618013^[16].

Body

Works and Contributions

Kakutani fixed-point theorem is credited with the discovery of Shizuo Kakutani^[3].

Why It Matters

Kakutani fixed-point theorem draws 122 Wikipedia views per month (fixed_point_theorem category, ranking #3 of 14).^[2] It has Wikipedia articles in 13 language editions, a strong signal of global cultural recognition.^[17] It is known by 3 alternative names across languages and contexts.^[18]