KnowraKakutani fixed-point theoremLinked fromLinked fromThe 7 pages that link to Kakutani fixed-point theorem, each with the reason it gives.All 7Broader topic 1Related 1Compared with 5Brouwer fixed-point theoremCompared with: It extends equilibrium arguments to set-valued maps rather than single-valued continuous maps.Fixed-point theoremBroader topic: It extends existence results from single-valued maps to set-valued correspondences.Banach fixed-point theoremCompared with: It extends fixed-point reasoning to correspondences rather than single-valued contractions.John NashRelated: Nash’s 1950 proof relied on this theorem to handle players’ sets of best responses.Schauder fixed-point theoremCompared with: It handles set-valued maps, whereas Schauder’s theorem concerns continuous functions.Sperner's lemmaCompared with: It extends fixed-point existence to set-valued maps, whereas Sperner’s statement is combinatorial.Ryll-Nardzewski fixed-point theoremCompared with: Kakutani concerns set-valued maps rather than distal semigroups of affine maps.