Note on improvements of order and efficiency in some iterative methods for solving nonlinear equations

A generalization of two modified iterative schemes for solving nonlinear equations suggested by Traub and Ezquerro et al. is presented. This new technique allows to obtain local order of convergence 2ρ+22ρ+2 from ρρ improving the above mentioned results where have been obtained ρ+1ρ+1 and 2ρ+12ρ+1 from ρρ respectively. The efficiency is also improved. New numerical algorithms of third and fourth order are used to check the theoretical result given. They are illustrated with numerical examples.