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A short proof of Fan's fixed point theorem


Author: Frode Terkelsen
Journal: Proc. Amer. Math. Soc. 42 (1974), 643-644
MSC: Primary 47H10
DOI: https://doi.org/10.1090/S0002-9939-1974-0333857-8
MathSciNet review: 0333857
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Abstract: Fan's fixed point theorem for multivalued functions in locally convex spaces is proved by means of Brouwer's fixed point theorem and the concept of a partition of unity.


References [Enhancements On Off] (What's this?)

  • [1] F. E. Browder, The fixed point theory of multi-valued mappings in topological vector spaces, Math. Ann. 177 (1968), 283-301. MR 37 #4679. MR 0229101 (37:4679)
  • [2] K. Fan, Fixed-point and minimax theorems in locally convex topological linear spaces, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 121-126. MR 13, 858. MR 0047317 (13:858d)
  • [3] S. Kakutani, A generalization of Brouwer's fixed point theorem, Duke Math. J. 8 (1941), 457-459. MR 3, 60. MR 0004776 (3:60c)
  • [4] A. Tychonoff, Ein Fixpunktsatz, Math. Ann. 111 (1935), 767-776. MR 1513031

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DOI: https://doi.org/10.1090/S0002-9939-1974-0333857-8
Article copyright: © Copyright 1974 American Mathematical Society

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