In this paper, we suggest anew iterative method for finding fixed points of a certain
class ofquasi-contractive operators defined in a closed, convexsubset of a Banach space.
Weprove that the convergence of this new iteration is equivalent to the c
onvergence
of (Mann,Ishikawa, Noor, (5)) iteration when we use the mapping(contractive-Like
operator).
Also We prove that the new iteration, is faster than the(Noor , Ishikawa ,Mann)
iteration method but the process (5) is faster than the new process for this class of
operators .
