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

This manuscript presents a developed fourth-order iterative familyof methods for determining the zero of nonlinear equations that isoptimal in line with Kung-Traub conjecture. The family of methodswas constructed by using weight function technique. One iterationcycle of any concrete member of the family of methods requires theevaluation of three functions. Consequently, the efficiency index of anyconcrete member of the family is 1.5873. The method convergenceanalysis was carried out via the Taylor series technique and numericalexamples are provided to illustrate its performance as compared withits contemporary existing methods for obtaining the zero of nonlinearequation.