Abstract
A Banach space has the weak fixed point property if its dual space has a weak ∗ sequentially compact unit ball and the dual space satisfies the weak ∗ uniform Kadec–Klee property; and it has the fixed point property if there exists ε > 0 such that, for every infinite subset A of the unit sphere of the dual space, A ∪ ( − A ) fails to be ( 2 − ε ) -separated. In particular, E-convex Banach spaces, a class of spaces that includes the uniformly nonsquare spaces, have the fixed point property.
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