{"id":224833,"date":"2025-11-10T08:15:50","date_gmt":"2025-11-10T14:15:50","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2025\/11\/kakutani-fixed-point-theorem"},"modified":"2025-11-10T08:15:50","modified_gmt":"2025-11-10T14:15:50","slug":"kakutani-fixed-point-theorem","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2025\/11\/kakutani-fixed-point-theorem","title":{"rendered":"Kakutani fixed-point theorem"},"content":{"rendered":"<p><a class=\"blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/kakutani-fixed-point-theorem2.jpg\"><\/a><\/p>\n<p>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 the 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\u2019s theorem extends this to set-valued functions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>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 [\u2026]<\/p>\n","protected":false},"author":709,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2229,8],"tags":[],"class_list":["post-224833","post","type-post","status-publish","format-standard","hentry","category-mathematics","category-space"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/224833","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/709"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=224833"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/224833\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=224833"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=224833"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=224833"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}