Semilocal Convergence Analysis of a Fourth-order Method in Banach Spaces and its Dynamics

摘要

In this paper, we study the semilocal convergence for a fourth-order method for solving nonlinear equations in Banach spaces by using recurrence relations. The recurrence relations for the method are derived and then an existence-uniqueness theorem has been proved. The basins of attraction of existing methods and the presented method are given to demonstrate their performance. AMS subject classification: 65D99.