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Stability of the fixed point property of Hilbert spaces
Author(s):
Pei-Kee
Lin
Journal:
Proc. Amer. Math. Soc.
127
(1999),
3573-3581.
MSC (1991):
Primary 47H09, 47H10
Posted:
May 6, 1999
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Abstract:
We prove that any Banach space  whose Banach-Mazur distance to a Hilbert space is less than  has the fixed point property for nonexpansive mappings.
References:
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- D. Alspach, A fixed point free nonexpansive map, Proc. Amer. Math. Soc. 82 (1981), 423-424. MR 82j:47070
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- A. G. Aksoy and M. A. Khamsi, Nonstandard Methods in Fixed Point Theory, Springer-Verlag, 1990. MR 91i:47073
- [DB]
- T. Domíngues Benavides, Stability of the fixed point property for nonexpansive mappings, Houston J. Math. (to appear).
- [ELOS]
- J. Elton, P. Lin, E. Odell and S. Szarek, Remarks on the fixed point problem for nonexpansive maps, Fixed points and Nonexpansive Mappings, Contemporary Math. Vol 18, Amer. Math. Soc., Princeton, 1983, pp. 87-120. MR 85d:47059
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- L. A. Karlovitz, Existence of fixed points of nonexpansive mappings in a space without normal structure, Pacific J. Math 66 (1976), 153-159. MR 55:8902
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- P.K. Lin, Unconditional Bases and fixed points of nonexpansive mappings, Pacific J. Math. 116 (1985), 69-76. MR 86c:47075
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- B. Maurey, Points fixes des contractions sur un convex fermé de
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Additional Information:
Pei-Kee
Lin
Affiliation:
Department of Mathematics, University of Memphis, Memphis, Tennessee 38152
Email:
linpk@mathsci.math.memphis.edu
DOI:
10.1090/S0002-9939-99-04971-0
PII:
S 0002-9939(99)04971-0
Received by editor(s):
January 28, 1997
Received by editor(s) in revised form:
February 16, 1998
Posted:
May 6, 1999
Additional Notes:
The work was done while the author was visiting the University of Texas at Austin. The author wishes to thank V. Mascioni, E. Odell and H. Rosenthal for their hospitality, particularly to V. Mascioni and E. Odell for their valuable discussion
Communicated by:
Dale E. Alspach
Copyright of article:
Copyright
1999,
American Mathematical Society
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