Stability of the fixed point property

of Hilbert spaces

Author:
Pei-Kee Lin

Journal:
Proc. Amer. Math. Soc. **127** (1999), 3573-3581

MSC (1991):
Primary 47H09, 47H10

DOI:
https://doi.org/10.1090/S0002-9939-99-04971-0

Published electronically:
May 6, 1999

MathSciNet review:
1616654

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

**[A]**D. Alspach,*A fixed point free nonexpansive map*, Proc. Amer. Math. Soc.**82**(1981), 423-424. MR**82j:47070****[AkK]**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****[GK]**K. Goebel and W. A. Kirk,*Topic in Metric Fixed Point Theory*, Cambridge Univ. Pres., 1990. MR**92c:47070****[JMLF]**A. Jiménez-Melado and E. Llorens-Fuster,*Opial modulus and stability of the fixed point property*, preprint.**[Ka]**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****[L]**P.K. Lin,*Unconditional Bases and fixed points of nonexpansive mappings*, Pacific J. Math.**116**(1985), 69-76. MR**86c:47075****[LiT]**J. Lindenstrauss and L. Tzafriri,*Classical Banach spaces I, Sequence spaces*, Springer, Berlin, 1977. MR**58:17766****[M]**B. Maurey,*Points fixes des contractions sur un convex fermé de*, Seminare d'Analyse Fonctionelle, Ecole Polytechnique, Palaiseau (1980-1981).

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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:
https://doi.org/10.1090/S0002-9939-99-04971-0

Received by editor(s):
January 28, 1997

Received by editor(s) in revised form:
February 16, 1998

Published electronically:
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

Article copyright:
© Copyright 1999
American Mathematical Society