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A SIMPLE PROOF OF THE SION MINIMAX THEOREM

박세희
대한수학회 (The Korean Mathematical Society)|2010.09|대한수학회보 (Bulletin of the KMS)|제47권 제5호|pp. 1037-1040

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참고문헌

키워드

KKM principleminimax theoremFan-Browder fixed point theorem
주제분류수학

초록

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.

Abstract

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.

참고문헌 (8)

  1. F. E. Browder, "The fixed point theory of multi-valued mappings in topological vector spaces", Math. Ann., 177, pp.283~301 (1968)
  2. Y. J. Cho, "Remarks on KKM maps and applications", J. Adv. Res. Appl. Math., 1(1), pp.1~8 (2009)
  3. K. Fan, "A generalization of Tychonoff's fixed point theorem", Math. Ann., 142, pp.305~310 (1960)
  4. J. Kindler, "A simple proof of Sion's minimax theorem", Amer. Math. Monthly, 112(4), pp.356~358 (2005)
  5. B. Knaster, "Ein Beweis des Fixpunktsatzes für n-Dimensionale Simplexe", Fund. Math., 14, pp.132~137 (1929)
  6. S. Park, "Ninety years of the Brouwer fixed point theorem", Vietnam J. Math., 27(3), pp.187~222 (1999)
  7. M. Sion, "On general minimax theorems", Pacific J. Math., 8, pp.171~176 (1958)
  8. J. von Neumann, "Zur Theorie der Gesellschaftsspiele", Math. Ann., 100(1), pp.295~320 (1928)

관련 논문AI추천

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