Convexity conditions and normal structure of Banach spaces

We prove that F-convexity, the property dual to P-convexity of Kottman, implies uniform normal structure. Moreover, in the presence of the WORTH property, normal structure follows from a weaker convexity condition than F-convexity. The latter result improves the known fact that every uniformly nonsquare space with the WORTH property has normal structure. © 2008 Elsevier Inc. All rights reserved