Proceedings of the American Mathematical Society

Author(s): J. García-Falset; A. Jiménez-Melado; E. Lloréns-Fuster
Journal: Proc. Amer. Math. Soc. 125 (1997), 2633-2636.
MSC (1991): Primary 47H09, 47H10
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Abstract: We show that for any renorming $\| \cdot \|$ of $\ell _{2}$ , the well known fixed point free mappings by Kakutani, Baillon and others are not nonexpansive.

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K. Goebel and W.A. Kirk Topics in metric fixed point theory. Cambridge Univ. Press 1990. MR 92c:47070

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K. Goebel, W.A. Kirk and R.L. Thele. Uniformly Lipschitzian semigroups in Hilbert space. Canad. J. Math. 26 (1974), 1245-1256. MR 50:10919

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Khamsi, M.A. Normal structure for Banach spaces with Schauder decomposition. Canad. Math. Bull. 33 (3), (1989), 1-8. MR 90i:46032

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D. Tingley Noncontractive uniformly Lipschitzian semigroups in Hilbert space, Proc. of Am. Math. Soc. 92, 3 (1984) (355-361). MR 85k:47105

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47H09, 47H10

J. García-Falset
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universitat de València, 46100 Burjassot, Valencia, Spain
Email: jesus.garcia@uv.es

A. Jiménez-Melado
Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain
Email: melado@ccuma.sci.uma.es

E. Lloréns-Fuster
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universitat de València, 46100 Burjassot, Valencia, Spain
Email: enrique.llorens@uv.es

DOI: 10.1090/S0002-9939-97-03845-8
PII: S 0002-9939(97)03845-8
Keywords: Nonexpansive mappings, uniformly lipschitzian mappings, fixed points
Received by editor(s): November 28, 1995
Received by editor(s) in revised form: March 18, 1996
Additional Notes: This research has been partially supported by D.G.I.C.Y.T. PB93-1177-C02-02 and D.G.I.C.Y.T. PB94-1496.
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1997, American Mathematical Society

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