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# The fixed point property in $\lowercase{c_0}$

Published:1998-12-01
Printed: Dec 1998
• Enrique Llorens-Fuster
• Brailey Sims
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## Abstract

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 $\fpp$.
 MSC Classifications: 47H09 - Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc. 47H10 - Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]