Property (M) and the weak fixed point property
Jesús Garcı́a Falset, Brailey Sims · Proceedings of the American Mathematical Society · 1997
It is shown that in Banach spaces with the property (M) of Kalton, nonexpansive self mappings of nonempty weakly compact convex sets necessarily have fixed points. The stability of this conclusion under renormings is examined and conditions for such spaces to have weak normal structure are considered.