# The fixed point property in c$_{\hbox {\bf 0}}$

Llorens-Fuster, Enrique and Sims, Brailey (1997) The fixed point property in c$_{\hbox {\bf 0}}$. [Preprint]

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We say a closed convex subset of the Banach space $(X,\|\cdot\|)$ has the {\sl fixed point property} (fpp) if every nonexpansive mapping $T:C\longrightarrow C$ has a fixed point. Here, $T$ nonexpansive means $\|Tx - Ty\| \leq \|x - y\|$, for all $x,\,y\in C$. We ask which nonempty closed bounded convex subsets of $c_0$ enjoy the fpp?