Semilocal convergence of a computationally efficient iterative method in Banach spaces under weak condition

Abstract

In this article, we discuss the semilocal convergence of well established efficient eighth-order method for solving nonlinear equations in Banach spaces under relaxed condition. The semilocal convergence of this scheme is established by using recurrence relations. We derive a system of recurrence relations for the method and then prove the existence and uniqueness result that shows the R-order of the method. Finally, numerical example is presented to validate the theoretical discussions.