|
Stability of the fixed point property in Hilbert spaces
Author(s):
Eva
María
Mazcuñán-Navarro
Journal:
Proc. Amer. Math. Soc.
134
(2006),
129-138.
MSC (2000):
Primary 47H10;
Secondary 46B20
Posted:
August 16, 2005
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper we prove that if  is a Banach space whose Banach-Mazur distance to a Hilbert space is less than  , then  has the fixed point property for nonexpansive mappings.
References:
-
- 1.
- A.G. Aksoy and M.A. Khamsi, Nonstandard methods in fixed point theory, Springer-Verlag, Berlin, 1990. MR 1066202 (91i:47073)
- 2.
- D. Alspach, A fixed point free nonexpansive map, Proc. Amer. Math. Soc. 82 (1981), 423-424. MR 0612733 (82j:47070)
- 3.
- M.M. Day, R.C. James, and S. Swaminathan, Normed linear spaces that are uniformly convex in every direction, Canad. J. Math. 23 (1971), 1051-1059. MR 0287285 (44:4492)
- 4.
- K. Goebel, On the structure of the minimal invariant sets for nonexpansive mappings, Annal. Univ. Mariae Curie-Sk
 odowska 29 (1975), 73-77. MR 0461226 (57:1211) - 5.
- L.A. Karlovitz, Existence of a fixed point for a nonexpansive map in a space without normal structure, Pacific J. Math. 66 (1976), 153-159. MR 0435951 (55:8902)
- 6.
- W.A. Kirk and B. Sims, Handbook of metric fixed point theory, Kluwer Academic Publishers, Dordrecht, Hardbound, 2001. MR 1904271 (2003b:47002)
- 7.
- P.K. Lin, Stability of the fixed point property of Hilbert spaces, Proc. Amer. Math. Soc. 127 (1999), 3573-3581. MR 1616654 (2000b:47116)
- 8.
- -, Unconditional bases and fixed points of nonexpansive mappings, Pacific J. Math. 116
(1985), 69-76. MR 0769823 (86c:47075) - 9.
- B. Sims, Ultra-techniques in Banach space theory, Queen's Papers in Pure and Applied Mathematics, No. 60, Kingston, Canada, 1982. MR 0778727 (86h:46032)
- 10.
- V. Zizler, On some rotundity and smoothness properties of Banach spaces, Dissertationes Math. Rozprawy 87 (1971) 33p.+errata insert. MR 0300060 (45:9108)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
47H10,
46B20
Retrieve articles in all Journals with MSC
(2000):
47H10,
46B20
Additional Information:
Eva
María
Mazcuñán-Navarro
Affiliation:
Departamento de Análisis Matemático, Universidad de Valencia, Doctor Moliner 50, 46100 Burjassot, Valencia, Spain
Address at time of publication:
Departamento de Matemáticas, Escuela de Ingenierías Industrial e Informática, Universidad de León, Campus de Vegazana, 24071 León, Spain
Email:
Eva.M.Mazcunan@uv.es, dememn@unileon.es
DOI:
10.1090/S0002-9939-05-08344-9
PII:
S 0002-9939(05)08344-9
Received by editor(s):
December 17, 2003
Posted:
August 16, 2005
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org