Some renormings of Banach spaces with the weak fixed point property for nonexpansive mappings

In 2013, Jiménez-Melado and Llorens-Fuster proved that the renorming of l2, |x| = max{

x

2, p(x)}, where p is a seminorm on l2 satisfying certain conditions, has the weak fixed point property. In this paper, we generalize this result for a Banach space having normal structure and Schauder basis. From this, we derive that every Banach space having normal structure and Schauder basis has an equivalent renorming that lacks asymptotic normal structure but has the weak fixed point property.