Approximation of fixed points of quasi-contractive operators by newiterationmethod

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 convergence 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 .