Fixed point theorem for αα-nonexpansive mappings in Banach spaces

We introduce the class of αα-nonexpansive mappings in Banach spaces. This class contains the class of nonexpansive mappings and is related to the class of firmly nonexpansive mappings in Banach spaces. In addition, we obtain a fixed point theorem for αα-nonexpansive mappings in uniformly convex Banach spaces.