The existence of common fixed points of best approximation for noncommuting pairs with different types of nonexpansive mappings have been proved. We also obtain some results on common fixed points from the set of best simultaneous approximation for a map T which is asymptotically (G,S)-nonexpansive where (T,G) and (T,S) are not necessarily commuting pairs. The proved results generalize and extend several known results on the subject.
