Abstract. We suggest and analyze a family of multi-step iterative methods for solving nonlinear equations using the decomposition technique mainly due to Rafiq et al. [13].

Abstract. In this paper, we suggest and analyze a family of multi-step iterative methods which do not involve the high-order differentials of the function for solving nonlinear equations using a different type of decomposition (mainly due to Noor and Noor [15]). We also discuss the convergence of the new proposed methods. Several numerical examples are given to illustrate the efficiency and the performance of the new iterative method. Our results can be considered as an improvement and refinement of the previous results.