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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Fixed points of nonexpansive mappings in Banach lattices


Authors: M. A. Khamsi and Ph. Turpin
Journal: Proc. Amer. Math. Soc. 105 (1989), 102-110
MSC: Primary 47H10; Secondary 46B30
DOI: https://doi.org/10.1090/S0002-9939-1989-0973841-5
MathSciNet review: 973841
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Abstract: We prove the existence of a fixed point for a nonexpansive mapping operating in a convex subset of a Banach lattice $ E$ compact for some natural topology $ \tau $ on $ E$. In particular, if $ E$ is a Banach space with a $ 1$-unconditional basis we can take for $ \tau $ the topology of coordinatewise convergence.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0973841-5
Article copyright: © Copyright 1989 American Mathematical Society