A Traub type result for one-point iterative methods with memory

Abstract

We present an extension of a well-known result of Traub to increase the R-order of convergence of one-point iterative methods by a simple modification of this type of methods. We consider the extension to one-point iterative methods with memory and present a particular case where Kurchatov's method is used. Moreover, we analyze the efficiency and the semilocal convergence of this method. Finally, two applications are presented, where differentiable and nondifferentiable equations are considered, that illustrate the above-mentioned.