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- Q518524 subject Q10129919.
- Q518524 subject Q8460852.
- Q518524 subject Q8482177.
- Q518524 subject Q8611989.
- Q518524 subject Q8612002.
- Q518524 subject Q8851971.
- Q518524 abstract "In mathematical analysis, the Kakutani fixed-point theorem is a fixed-point theorem for set-valued functions. It provides sufficient conditions for a set-valued function defined on a convex, compact subset of a Euclidean space to have a fixed point, i.e. a point which is mapped to a set containing it. The Kakutani fixed point theorem is a generalization of Brouwer fixed point theorem. The Brouwer fixed point theorem is a fundamental result in topology which proves the existence of fixed points for continuous functions defined on compact, convex subsets of Euclidean spaces. Kakutani's theorem extends this to set-valued functions.The theorem was developed by Shizuo Kakutani in 1941, and was used by John Nash in his description of Nash equilibria. It has subsequently found widespread application in game theory and economics.".
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- Q518524 type Thing.
- Q518524 comment "In mathematical analysis, the Kakutani fixed-point theorem is a fixed-point theorem for set-valued functions. It provides sufficient conditions for a set-valued function defined on a convex, compact subset of a Euclidean space to have a fixed point, i.e. a point which is mapped to a set containing it. The Kakutani fixed point theorem is a generalization of Brouwer fixed point theorem.".
- Q518524 label "Kakutani fixed-point theorem".
- Q518524 seeAlso Q282640.
- Q518524 seeAlso Q44455.
- Q518524 seeAlso Q747534.