Fixed points of nonexpansive mappings in Banach lattices

Khamsi, M. A.; Turpin, Ph.

doi:10.1090/S0002-9939-1989-0973841-5

Fixed points of nonexpansive mappings in Banach lattices
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by M. A. Khamsi and Ph. Turpin PDF

Proc. Amer. Math. Soc. 105 (1989), 102-110 Request permission

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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