We consider a mapping S of the form S = α 0 I + α 1 T 1 + α 2 T 2 + ⋯ + α k T k , where α i ≥ 0 , α 0 > 0 , α 1 > 0 and ∑ i = 0 k α i = 1 . We show that the Picard iterates of S converge to a common fixed point of T i ( i = 1 , 2 , … , k ) in a Banach space when T i ( i = 1 , 2 , … , k ) are nonexpansive.