Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-26T08:07:28.938Z Has data issue: false hasContentIssue false
  • English
  • Français

Normal structure and fixed point property

Published online by Cambridge University Press:  18 May 2009

J. García-Falset  and
E. Lloréns-Fuster
J. García-Falset
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Doctor Moliner, 50, 46100 Burjasot, Valencia, Spain
E. Lloréns-Fuster
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Doctor Moliner, 50, 46100 Burjasot, Valencia, Spain
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The most classical sufficient condition for the fixed point property of non-expansive mappings FPP in Banach spaces is the normal structure (see [6] and [10]). (See definitions below). Although the normal structure is preserved under finite lp-product of Banach spaces, (1<p≤∞), (see Landes, [12], [13]), not too many positive results are known about the normal structure of an l1,-product of two Banach spaces with this property. In fact, this question was explicitly raised by T. Landes [12], and M. A. Khamsi [9] and T. Domíinguez Benavides [1] proved partial affirmative answers. Here we give wider conditions yielding normal structure for the product X1⊗1X2.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 38 , Issue 1 , January 1996 , pp. 29 - 37
Copyright
Copyright © Glasgow Mathematical Journal Trust 1996

References

REFERENCES

1.Benavides, T. Domíinguez, Weak uniform normal structure in direct sum spaces. Studia Math. 103,(3), (1992), 283–290.CrossRefGoogle Scholar
2.Benavides, T. Domínguez, Acedo, G. Lóopez and Xu, H. K., Weak uniform normal structure and construction fixed points of nonexpansive mappings. Preprint.Google Scholar
3.van Dulst, D. and Sims, B., Fixed points of nonexpansive mappings and Chebyshev centers in Banach space with norms of type (KK) in Banach Space Theory and Its Applications (Bucharest, 1981), Lecture Notes in Math. 991 (Springer-Verlag, 1983), 35–43.CrossRefGoogle Scholar
4.García-Falset, J., Jiménez-Melado, A. and Lloréns-Fuster, E., A characterization of normal structure in Proceedings of Second International Conference on Fixed Point Theory and Appl.Halifax, 1991, (World Scientific, Singapore, 1992), 122–129.Google Scholar
5.García-Falset, J., Jiméenez-Melado, A. and Llorens-Fuster, E., Measures of noncompactness and normal structure in Banach spaces. Studia Math. 110, (1), (1994), 1–8.CrossRefGoogle Scholar
6.Goebel, K. and Kirk, W. A., Topics in metric fixed point theory (Cambridge University Press, 1990).CrossRefGoogle Scholar
7.Gossez, J. P. and Dozo, E. Lami. Some geometrical properties related to the fixed-point theory for nonexpansive mappings, Pacific J. Math. 40 (1972), 565–573.CrossRefGoogle Scholar
8.Jiménez-Melado, A., Stability of weak normal structure in James quasi reflexive space, Bull.Austral. Math. Soc. 46 (1992), 367–372.CrossRefGoogle Scholar
9.Khamsi, M. A., Normal structure for Banach spaces with Schauder decomposition, Canad.Math. Bull. 32 (3), (1989), 344–351.CrossRefGoogle Scholar
10.Kirk, W. A., A fixed point theorem for mappings which do not increase distances, Amer.Math. Monthly 72 (1965), 1004–1006.CrossRefGoogle Scholar
11.Kuczumow, T., Reich, S. and Schmidt, M., A fixed point property of l 1product spaces, Proc.Amer. Math. Soc. 119 (2), (1993), 457–463.Google Scholar
12.Landes, T., Permanence properties of normal structure, Pacific J. Math. 110, 1, (1984), 125–143.CrossRefGoogle Scholar
13.Landes, T., Normal structure and the sum property, Pacific J. Math. 123 (1986), 127–147.CrossRefGoogle Scholar
14.Tingley, D., The normal structure of James quasi reflexive space, Bull. Austral. Math. Soc. 42, (1990), 95–100.CrossRefGoogle Scholar