  We show that the super fixed point property for nonexpansive mappings and for
asymptotically nonexpansive mappings in the intermediate sense are equivalent.
As a consequence, we obtain fixed point theorems for asymptotically
nonexpansive mappings in uniformly nonsquare and uniformly noncreasy Banach
spaces. The results are generalized for commuting families of asymptotically
nonexpansive mappings.
