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On the converse of the nonexpansive map fixed point theorem for Hilbert space

Author: Robert Sine
Journal: Proc. Amer. Math. Soc. 100 (1987), 489-490
MSC: Primary 47H15
MathSciNet review: 891152
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Abstract: A simple proof is given of Ray's theorem that a nonempty, closed, convex, and unbounded set in Hilbert space admits a fixed point free nonexpansive map.

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

  • [1] F. E. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1041-1044. MR 0187120 (32:4574)
  • [2] D. Göhde, Zum Prinzep der Kontractiven Abbildung, Math. Nachr. 30 (1965), 251-258. MR 0190718 (32:8129)
  • [3] W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004-1006. MR 0189009 (32:6436)
  • [4] W. O. Ray, The fixed point property and unbounded sets in Hilbert space, Tran. Amer. Math. Soc. 258 (1980), 531-537. MR 558189 (81e:47044)

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Article copyright: © Copyright 1987 American Mathematical Society

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