The property WORTH* and the weak fixed point property

A Banach space, $X$, has the weak fixed point property (w-FPP) if every nonexpansive mapping, $T$, on every weak compact convex nonempty subset, $C$, has a fixed point. A Banach space, $X^*$, has WORTH* if for every weak* null sequence $(x^*_n)$ and every $x^* \in X^*$, \[\limsup_n\|x^*_n-x^*\|=\limsup_n\|x^*_n+x^*\|.\] A new proof is given of the recent result that WORTH* implies the weak fixed point property