On the super fixed point property in product spaces

We prove that if F is a finite-dimensional Banach space and X has the super fixed point property for nonexpansive mappings, then F⊕X has the super fixed point property with respect to a large class of norms including all lp norms, 1⩽p<∞. This provides a solution to the “super-version” of the problem of Khamsi (1989).