On the Behavior of the Four Order Iteration in Euler's Family Near a Zero (Journal of Mathematical Study, 2018)
The aim of this paper is to study the local convergence of the four orderiteration of Euler's family for solving nonlinear operator equations. We get the optimalradius of the local convergence ball of the method for operators satisfying the weakthird order generalized Lipschitz condition with L-average. We also show that thelocal convergence of the method is determined by a period 2 orbit of the method itselfapplied to a real function.