A local convergence analysis for a generalization of a family of Ste ensen-type iterative methods with three frozen steps is presented for solving nonlinear equations. From the use of three classical divided di erence operators, we study four families of iterative methods with optimal local order of convergence. Then, new variants of the family of iterative methods is constructed, where a study of the computational e ciency is carried out. Moreover, the semilocal convergence for these families is also studied. Finally, an application of nonlinear integral equations of mixed Hammerstein type is presented, where multiple precision and a stopping criterion are implemented without using any known root. In addition, a study, where we compare orders, e ciencies and elapsed times of the methods suggested, supports the theoretical results obtained.