Kakutani fixed-point theorem

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. Article "Kakutani fixed-point theorem" in English Wikipedia has 44.2 points for quality (as of July 1, 2025). The article contains 17 references and 22 sections.

In this language version of Wikipedia the article has the best quality. Also, this article is the most popular in that language version.

Since the creation of article "Kakutani fixed-point theorem", its content was written by 69 registered users of English Wikipedia and edited by 183 registered Wikipedia users in all languages.

The article is cited 670 times in English Wikipedia and cited 950 times in all languages.

The highest Authors Interest rank from 2001:

• Local (English): #49761 in September 2005
• Global: #82058 in May 2017

The highest popularity rank from 2008:

• Local (English): #327314 in November 2014
• Global: #306629 in April 2022

There are 14 language versions for this article in the WikiRank database (of the considered 55 Wikipedia language editions).

The quality and popularity assessment was based on Wikipédia dumps from July 1, 2025 (including revision history and pageviews for previous years).

The table below shows the language versions of the article with the highest quality.

#	Language	Quality grade	Quality score
1	English (en) Kakutani fixed-point theorem		44.1594
2	Chinese (zh) 角谷不动点定理		32.0643
3	French (fr) Théorème du point fixe de Kakutani		28.664
4	German (de) Fixpunktsatz von Kakutani		25.6647
5	Korean (ko) 가쿠타니 사상		24.4314
6	Japanese (ja) 角谷の不動点定理		22.3819
7	Russian (ru) Теорема Какутани о неподвижной точке		14.5961
8	Portuguese (pt) Teorema do ponto fixo de Kakutani		13.9013
9	Hebrew (he) משפט נקודת השבת של קאקוטאני		12.5589
10	Ukrainian (uk) Теорема Какутані про нерухому точку		10.3089

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The following table shows the most popular language versions of the article.

The most popular language versions of the article "Kakutani fixed-point theorem" in all the time

#	Language	Popularity award	Relative popularity
1	English (en) Kakutani fixed-point theorem		377 632
2	Japanese (ja) 角谷の不動点定理		40 810
3	French (fr) Théorème du point fixe de Kakutani		38 301
4	Spanish (es) Teorema del punto fijo de Kakutani		26 420
5	Italian (it) Teorema di Kakutani		23 046
6	Russian (ru) Теорема Какутани о неподвижной точке		17 471
7	German (de) Fixpunktsatz von Kakutani		16 854
8	Chinese (zh) 角谷不动点定理		15 921
9	Portuguese (pt) Teorema do ponto fixo de Kakutani		8 054
10	Korean (ko) 가쿠타니 사상		2 586

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The following table shows the language versions of the article with the highest popularity in the last month.

The most popular language versions of the article "Kakutani fixed-point theorem" in June 2025

#	Language	Popularity award	Relative popularity
1	English (en) Kakutani fixed-point theorem		1 592
2	Japanese (ja) 角谷の不動点定理		300
3	Chinese (zh) 角谷不动点定理		200
4	French (fr) Théorème du point fixe de Kakutani		165
5	Russian (ru) Теорема Какутани о неподвижной точке		154
6	Italian (it) Teorema di Kakutani		103
7	Spanish (es) Teorema del punto fijo de Kakutani		71
8	German (de) Fixpunktsatz von Kakutani		67
9	Portuguese (pt) Teorema do ponto fixo de Kakutani		40
10	Korean (ko) 가쿠타니 사상		33

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The following table shows the language versions of the article with the highest Authors’ Interest.

Language versions of the article "Kakutani fixed-point theorem" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.

#	Language	AI award	Relative AI
1	English (en) Kakutani fixed-point theorem		69
2	Italian (it) Teorema di Kakutani		24
3	French (fr) Théorème du point fixe de Kakutani		11
4	Spanish (es) Teorema del punto fijo de Kakutani		10
5	German (de) Fixpunktsatz von Kakutani		9
6	Russian (ru) Теорема Какутани о неподвижной точке		9
7	Chinese (zh) 角谷不动点定理		9
8	Hebrew (he) משפט נקודת השבת של קאקוטאני		8
9	Dutch (nl) Dekpuntstelling van Kakutani		7
10	Portuguese (pt) Teorema do ponto fixo de Kakutani		7

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The following table shows the language versions of the article with the highest Authors’ Interest in the last month.

Language versions of the article "Kakutani fixed-point theorem" with the highest AI in June 2025

#	Language	AI award	Relative AI
1	Catalan (ca) Teorema del punt fix de Kakutani		0
2	German (de) Fixpunktsatz von Kakutani		0
3	English (en) Kakutani fixed-point theorem		0
4	Spanish (es) Teorema del punto fijo de Kakutani		0
5	French (fr) Théorème du point fixe de Kakutani		0
6	Hebrew (he) משפט נקודת השבת של קאקוטאני		0
7	Italian (it) Teorema di Kakutani		0
8	Japanese (ja) 角谷の不動点定理		0
9	Korean (ko) 가쿠타니 사상		0
10	Dutch (nl) Dekpuntstelling van Kakutani		0

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The following table shows the language versions of the article with the highest number of citations.

Language versions of the article "Kakutani fixed-point theorem" with the highest Citation Index (CI)

#	Language	CI award	Relative CI
1	English (en) Kakutani fixed-point theorem		670
2	Chinese (zh) 角谷不动点定理		96
3	Japanese (ja) 角谷の不動点定理		58
4	Korean (ko) 가쿠타니 사상		34
5	Ukrainian (uk) Теорема Какутані про нерухому точку		31
6	French (fr) Théorème du point fixe de Kakutani		15
7	Spanish (es) Teorema del punto fijo de Kakutani		11
8	Italian (it) Teorema di Kakutani		8
9	German (de) Fixpunktsatz von Kakutani		7
10	Portuguese (pt) Teorema do ponto fixo de Kakutani		6

More...

#	Language	Value
ca	Catalan Teorema del punt fix de Kakutani
de	German Fixpunktsatz von Kakutani
en	English Kakutani fixed-point theorem
es	Spanish Teorema del punto fijo de Kakutani
fr	French Théorème du point fixe de Kakutani
he	Hebrew משפט נקודת השבת של קאקוטאני
it	Italian Teorema di Kakutani
ja	Japanese 角谷の不動点定理
ko	Korean 가쿠타니 사상
nl	Dutch Dekpuntstelling van Kakutani
pt	Portuguese Teorema do ponto fixo de Kakutani
ru	Russian Теорема Какутани о неподвижной точке
uk	Ukrainian Теорема Какутані про нерухому точку
zh	Chinese 角谷不动点定理

Best Rank

English: #327314 11.2014

Global: #306629 04.2022

Best Rank

English: #49761 09.2005

Global: #82058 05.2017

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The WikiRank project is intended for automatic relative evaluation of the articles in the various language versions of Wikipedia. At the moment the service allows to compare over 44 million Wikipedia articles in 55 languages. Quality scores of articles are based on Wikipedia dumps from July, 2025. When calculating current popularity and AI of articles data from June 2025 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2025... More information