Canad. Math. Bull. 41(1998), 413-422
Printed: Dec 1998
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 $\fpp$.
47H09 - Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc.
47H10 - Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]