Approximating fixed points of nonexpansive and generalized nonexpansive mappings

In this paper we consider a mapping S of the form S=α0I+α1T+α2T2+…+αKTK, where αi≥0. α1>0 with ∑i=0kαi=1, and show that in a uniformly convex Banach space the Picard iterates of S converge to a fixed point of T when T is nonexpansive or generalized nonexpansive or even quasinonexpansive