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The Fixed Point Property in c0

Published online by Cambridge University Press:  20 November 2018

Enrique Llorens-Fuster  and
Brailey Sims
Enrique Llorens-Fuster
Affiliation:
Departament d’Anàlisi Matematica Facultat de Matematiques Universitat de València Doctor Moliner 50 46100 Burjassot Spain
Brailey Sims
Affiliation:
Department of Mathematics The University of Newcastle NSW 2308 Australia
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Abstract

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A closed convex subset of ${{c}_{0}}$ has the fixed point property (fpp) if every nonexpansive self mapping of it has a fixed point. All nonempty weak compact convex subsets of ${{c}_{0}}$ are known to have the fpp. We show that closed convex subsets with a nonempty interior and nonempty convex subsets which are compact in a topology slightly coarser than the weak topology may fail to have the fpp.

Keywords

47H0947H10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 4 , 01 December 1998 , pp. 413 - 422
Copyright
Copyright © Canadian Mathematical Society 1998

References

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