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For convex subsets X of a topological vector space E, we show that a KKM principle implies a Fan-Browder type fixed point theorem and that this theorem implies generalized forms of the Sion minimax theorem.
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참고문헌 (8)
참고문헌 신청
B. Knaster / 1929 / Ein Beweis des Fixpunktsatzes fur n-Dimensionale Simplexe / Fund. Math. 14 : 132 ~ 137
F. E. Browder / 1968 / The fixed point theory of multi-valued mappings in topological vector spaces / Math. Ann. 177 : 283 ~ 301
J. Kindler / 2005 / A simple proof of Sion's minimax theorem / Amer. Math. Monthly 112 (4) : 356 ~ 358
J. von Neumann / 1928 / Zur Theorie der Gesellschaftsspiele / Math. Ann. 100 (1) : 295 ~ 320
K. Fan / 1960 / A generalization of Tychonoff's fixed point theorem / Math. Ann. 142 : 305 ~ 310
F. E. Browder / 1968 / The fixed point theory of multi-valued mappings in topological vector spaces / Math. Ann. 177 : 283 ~ 301
J. Kindler / 2005 / A simple proof of Sion's minimax theorem / Amer. Math. Monthly 112 (4) : 356 ~ 358
J. von Neumann / 1928 / Zur Theorie der Gesellschaftsspiele / Math. Ann. 100 (1) : 295 ~ 320
K. Fan / 1960 / A generalization of Tychonoff's fixed point theorem / Math. Ann. 142 : 305 ~ 310
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