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- Q518524 description "mathematischer Satz" @default.
- Q518524 description "teorema de topologia" @default.
- Q518524 description "teoremo ke fikspunkton havas funkcio f: S→Pow(S) sur kompakta nemalplena konveksa subaro S⊂ℝⁿ, kies grafo estas fermita kaj kies bildo f(x) is estas nemalplena kaj konveksa por ĉiu x∈S" @default.
- Q518524 description "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" @default.
- Q518524 description "משפט באנליזה פונקציונלית" @default.
- Q518524 description "定理" @default.
- Q518524 name "Dekpuntstelling van Kakutani" @default.
- Q518524 name "Fixpunktsatz von Kakutani" @default.
- Q518524 name "Kakutani fixed-point theorem" @default.
- Q518524 name "Teorema del punt fix de Kakutani" @default.
- Q518524 name "Teorema do ponto fixo de Kakutani" @default.
- Q518524 name "fikspunkta teoremo de Kakutani" @default.
- Q518524 name "teorema del punto fijo de Kakutani" @default.
- Q518524 name "teorema di Kakutani" @default.
- Q518524 name "théorème du point fixe de Kakutani" @default.
- Q518524 name "Теорема Какутани о неподвижной точке" @default.
- Q518524 name "Теорема Какутані про нерухому точку" @default.
- Q518524 name "משפט נקודת השבת של קאוקטאני" @default.
- Q518524 name "角谷の不動点定理" @default.
- Q518524 name "角谷静夫不动点定理" @default.
- Q518524 name "角谷静夫不动点定理" @default.
- Q518524 name "角谷靜夫不動點定理" @default.
- Q518524 name "가쿠타니 사상" @default.
- Q518524 type Item @default.
- Q518524 label "Dekpuntstelling van Kakutani" @default.
- Q518524 label "Fixpunktsatz von Kakutani" @default.
- Q518524 label "Kakutani fixed-point theorem" @default.
- Q518524 label "Teorema del punt fix de Kakutani" @default.
- Q518524 label "Teorema do ponto fixo de Kakutani" @default.
- Q518524 label "fikspunkta teoremo de Kakutani" @default.
- Q518524 label "teorema del punto fijo de Kakutani" @default.
- Q518524 label "teorema di Kakutani" @default.
- Q518524 label "théorème du point fixe de Kakutani" @default.
- Q518524 label "Теорема Какутани о неподвижной точке" @default.
- Q518524 label "Теорема Какутані про нерухому точку" @default.
- Q518524 label "משפט נקודת השבת של קאוקטאני" @default.
- Q518524 label "角谷の不動点定理" @default.
- Q518524 label "角谷静夫不动点定理" @default.
- Q518524 label "角谷静夫不动点定理" @default.
- Q518524 label "角谷靜夫不動點定理" @default.
- Q518524 label "가쿠타니 사상" @default.
- Q518524 altLabel "角谷不动点定理" @default.
- Q518524 altLabel "角谷不動點定理" @default.
- Q518524 altLabel "角谷定點定理" @default.
- Q518524 prefLabel "Dekpuntstelling van Kakutani" @default.
- Q518524 prefLabel "Fixpunktsatz von Kakutani" @default.
- Q518524 prefLabel "Kakutani fixed-point theorem" @default.
- Q518524 prefLabel "Teorema del punt fix de Kakutani" @default.
- Q518524 prefLabel "Teorema do ponto fixo de Kakutani" @default.
- Q518524 prefLabel "fikspunkta teoremo de Kakutani" @default.
- Q518524 prefLabel "teorema del punto fijo de Kakutani" @default.
- Q518524 prefLabel "teorema di Kakutani" @default.
- Q518524 prefLabel "théorème du point fixe de Kakutani" @default.
- Q518524 prefLabel "Теорема Какутани о неподвижной точке" @default.
- Q518524 prefLabel "Теорема Какутані про нерухому точку" @default.
- Q518524 prefLabel "משפט נקודת השבת של קאוקטאני" @default.
- Q518524 prefLabel "角谷の不動点定理" @default.
- Q518524 prefLabel "角谷静夫不动点定理" @default.
- Q518524 prefLabel "角谷静夫不动点定理" @default.
- Q518524 prefLabel "角谷靜夫不動點定理" @default.
- Q518524 prefLabel "가쿠타니 사상" @default.
- Q518524 P10283 Q518524-56290652-B9F9-4875-B9C8-4F6B0C5BB939 @default.
- Q518524 P138 Q518524-0a0999f4-4582-c33e-54e2-7f95571c6a51 @default.
- Q518524 P2534 Q518524-31958107-42ff-4493-203c-316ee57319d8 @default.
- Q518524 P279 Q518524-6472c339-4c66-a27f-0969-244fefd6d399 @default.
- Q518524 P31 Q518524-200ce832-4bd0-0056-6653-c3aa8cadd9ac @default.
- Q518524 P3827 Q518524-DD409DB9-E500-48D3-943A-67DEE44A750A @default.
- Q518524 P575 Q518524-cc259758-42f2-00e4-3325-3afe4bfb2b69 @default.
- Q518524 P61 Q518524-ec568aac-467d-fc46-b61c-1dfd034c4b95 @default.
- Q518524 P6104 Q518524-E0B79562-1AFF-42C3-8E25-94EA6C814F14 @default.
- Q518524 P6366 Q518524-59261460-024A-4FD7-8F3E-5F47DAB870CD @default.
- Q518524 P646 Q518524-73C207EE-7ACB-44B0-A1B6-006EF902CDF1 @default.
- Q518524 P6366 134618013 @default.
- Q518524 P10283 "C134618013" @default.
- Q518524 P138 Q945209 @default.
- Q518524 P2534 "<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\begin{aligned}&f\colon S\to \operatorname {Pow} (S)\\&S\subset \mathbb {R} ^{n}\\&S\neq \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)\neq \varnothing \land \operatorname {conv} (f(x))=f(x))\right)\implies \exists s\in S\colon s\in \phi (s)\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd /> <mtd> <mi>f</mi> <mo>:<!-- : --></mo> <mi>S</mi> <mo stretchy="false">→<!-- → --></mo> <mi>Pow</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <mi>S</mi> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi>S</mi> <mo>⊂<!-- ⊂ --></mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi>S</mi> <mo>≠<!-- ≠ --></mo> <mi class="MJX-variant">∅<!-- ∅ --></mi> <mo>∧<!-- ∧ --></mo> <mi>conv</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <mi>S</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>cl</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <mi>S</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>S</mi> <mo>∧<!-- ∧ --></mo> <munder> <mo movablelimits="true" form="prefix">sup</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo>∈<!-- ∈ --></mo> <mi>S</mi> </mrow> </munder> <mo fence="false" stretchy="false">‖<!-- ‖ --></mo> <mi>s</mi> <mo fence="false" stretchy="false">‖<!-- ‖ --></mo> <mo><</mo> <mi mathvariant="normal">∞<!-- ∞ --></mi> <mo>∧<!-- ∧ --></mo> <mo fence="false" stretchy="false">{</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>:<!-- : --></mo> <mi>y</mi> <mo>∈<!-- ∈ --></mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">}</mo> <mo>=</mo> <mi>cl</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <mo fence="false" stretchy="false">{</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>:<!-- : --></mo> <mi>y</mi> <mo>∈<!-- ∈ --></mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">}</mo> <mo stretchy="false">)</mo> <mo>∧<!-- ∧ --></mo> <mrow> <mo>(</mo> <mrow> <mi mathvariant="normal">∀<!-- ∀ --></mi> <mi>x</mi> <mo>∈<!-- ∈ --></mo> <mi>S</mi> <mo>:<!-- : --></mo> <mo stretchy="false">(</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>≠<!-- ≠ --></mo> <mi class="MJX-variant">∅<!-- ∅ --></mi> <mo>∧<!-- ∧ --></mo> <mi>conv</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> <mspace width="thickmathspace" /> <mo stretchy="false">⟹<!-- ⟹ --></mo> <mspace width="thickmathspace" /> <mi mathvariant="normal">∃<!-- ∃ --></mi> <mi>s</mi> <mo>∈<!-- ∈ --></mo> <mi>S</mi> <mo>:<!-- : --></mo> <mi>s</mi> <mo>∈<!-- ∈ --></mo> <mi>ϕ<!-- ϕ --></mi> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}&f\colon S\to \operatorname {Pow} (S)\\&S\subset \mathbb {R} ^{n}\\&S\neq \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)\neq \varnothing \land \operatorname {conv} (f(x))=f(x))\right)\implies \exists s\in S\colon s\in \phi (s)\end{aligned}}}</annotation> </semantics> </math>" @default.
- Q518524 P279 Q17089994 @default.
- Q518524 P31 Q1422068 @default.
- Q518524 P3827 "kakutani-theorem" @default.
- Q518524 P575 "1938-01-01T00:00:00Z" @default.
- Q518524 P61 Q945209 @default.
- Q518524 P6104 Q8487137 @default.
- Q518524 P6366 "134618013" @default.
- Q518524 P646 "/m/07vxx7" @default.