On the converse of the nonexpansive map fixed point theorem for Hilbert space
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- by Robert Sine PDF
- Proc. Amer. Math. Soc. 100 (1987), 489-490 Request permission
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
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- W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004–1006. MR 189009, DOI 10.2307/2313345
- William O. Ray, The fixed point property and unbounded sets in Hilbert space, Trans. Amer. Math. Soc. 258 (1980), no. 2, 531–537. MR 558189, DOI 10.1090/S0002-9947-1980-0558189-1
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 100 (1987), 489-490
- MSC: Primary 47H15
- DOI: https://doi.org/10.1090/S0002-9939-1987-0891152-1
- MathSciNet review: 891152