Semilocal Convergence of the Extension of Chun’s Method

Abstract

In this work, we use the technique of recurrence relations to prove the semilocal convergence in Banach spaces of the multidimensional extension of Chun’s iterative method. This is an iterative method of fourth order, that can be transferred to the multivariable case by using the divided difference operator. We obtain the domain of existence and uniqueness by taking a suitable starting point and imposing a Lipschitz condition to the first Fréchet derivative in the whole domain. Moreover, we apply the theoretical results obtained to a nonlinear integral equation of Hammerstein type, showing the applicability of our results.

Keywords

• nonlinear equations
• iterative methods
• divided difference
• semilocal convergence
• domain of existence and uniqueness
• hammerstein type nonlinear integral equations