an optimal family of methods for obtaining the zero of nonlinear equation

This manuscript presents a developed fourth-order iterative family of methods for determining the zero of nonlinear equations that is optimal in line with kung-traub conjecture. the family of methods was constructed by using weight function technique. one iteration cycle of any concrete member of the family of methods requires the evaluation of three functions. consequently, the efficiency index of any concrete member of the family is 1.5873. the method convergence analysis was carried out via the taylor series technique and numerical examples are provided to illustrate its performance as compared with its contemporary existing methods for obtaining the zero of nonlinear equation.