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The fixed point property in banach spaces whose characteristic of uniform convexity is less than 2

Part of: Nonlinear operators and their properties

Published online by Cambridge University Press:  09 April 2009

J. García Falset
J. García Falset
Affiliation:
Department o de Análisis MatemáticoUniversidad de ValenciaDoctor Miliner 50 46.100 Burjassot, Spain
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Abstract

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We prove that every Banach space X with characteristic of uniform convexity less than 2 has the fixed point property whenever X satisfies a certain orthogonality condition.

MSC classification

Secondary: 47H10: Fixed-point theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 54 , Issue 2 , April 1993 , pp. 169 - 173
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Alspach, D., ‘A fixed point free nonexpansive map’, Proc. Amer. Soc. 82 (1981), 423–424.Google Scholar
[2]Borwein, J. M. and Sims, B., ‘Nonexpansive mapping on Banach lattices and related topics’, Houston J. Math. 10 (1984), 339–356.Google Scholar
[3]Elton, J. and Lin, P. K., Odell, E. and Szarek, S., ‘Remarks on the fixed point problem for nonexpansive maps’, Contemp. Math. 18 (1983), 87–120.CrossRefGoogle Scholar
[4]Falset, J. Garcia and Fuster, E. Llorens, ‘A geometric property of Banach spaces related to the fixed point property’, J. Math. Anal. Appl. to appear.Google Scholar
[5]Karlovitz, L. A., ‘Existence of fixed points for nonexpansive mappings in space without normal structure’, Pacific J. Math. 66 (1976), 153–159.Google Scholar
[6]Kirk, W. A., ‘A fixed point theorem for mappings which do not increase distance’, Amer. Math. Monthly 72 (1965), 1004–1006.Google Scholar
[7]Maurey, B., ‘Points fixes des contractions de L1 de certaines faiblement compacts’, in: Seminar on Functional Analysis, 1980–81 (Exp. No. VIII, École Polytech., Palgiseau, 1981).Google Scholar
[8]Sims, B., ‘Orthogonality and fixed points of nonexpansive maps’, Proc. Centre Math. Anal. Austral. Nat. Univ. 20 (1988), 178–186.Google Scholar