Fixed points of nonexpansive mappings in Banach lattices
Mohamed A. Khamsi, Ph. Turpin · Proceedings of the American Mathematical Society · 1989
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.