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A simple proof of a theorem of Ky Fan


Author: V. M. Sehgal
Journal: Proc. Amer. Math. Soc. 63 (1977), 368-369
MSC: Primary 47H10
DOI: https://doi.org/10.1090/S0002-9939-1977-0435954-8
MathSciNet review: 0435954
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Abstract: A simple proof of a fixed point theorem of Ky Fan in locally convex spaces is constructed by means of his fixed point theorem for set valued functions.


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

  • [1] James Dugundji, Topology, Allyn and Bacon, Boston, 1966. MR 33 #1824. MR 0193606 (33:1824)
  • [2] Ky 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] -, Extensions of two fixed point theorems of F. E. Browder, Math. Z. 112 (1969), 234-240. MR 40 #4830. MR 0251603 (40:4830)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0435954-8
Keywords: Fixed points, set valued mapping, upper and lower semicontinuity
Article copyright: © Copyright 1977 American Mathematical Society

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