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<identifier>oai:HAL:hal-00699225v1</identifier>
<datestamp>2017-12-21</datestamp>
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<publisher>HAL CCSD</publisher>
<title lang=en>Fixed points for Kakutani factorizable multifunctions</title>
<creator>Lassonde, Marc</creator>
<contributor>Laboratoire de Mathématiques Informatique et Applications (LAMIA) ; Université des Antilles et de la Guyane (UAG)</contributor>
<description>International audience</description>
<source>Journal of Mathematical Analysis and applications</source>
<publisher>Elsevier</publisher>
<identifier>hal-00699225</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00699225</identifier>
<source>https://hal.archives-ouvertes.fr/hal-00699225</source>
<source>Journal of Mathematical Analysis and applications, Elsevier, 1990, 152 (1), pp.46-60</source>
<language>en</language>
<subject>[MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA]</subject>
<type>info:eu-repo/semantics/article</type>
<type>Journal articles</type>
<description lang=en>A multifunction Γ is called a Kakutani multifunction if there exist two nonempty convex sets X and Y , each in a Hausdorff topological vector space, such that Γ : X → Y is upper semi-continuous with nonempty compact convex values. We prove the following extension of the Kakutani fixed point theorem : Let Γ : X → X be a multi-function from a simplex X into itself ; if Γ can be factorized by an arbitrary finite number of Kakutani multifunctions, then Γ has a fixed point. The proof relies on a simplicial approximation technique and the Brouwer fixed point theorem. Extensions to infinite-dimensional spaces and applications to game theory are given.</description>
<date>1990</date>
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