Semilocal convergence of a sixth-order method in Banach spaces

In this paper, we introduce a new iterative method of order six and study the semilocal convergence of the method by using the recurrence relations for solving nonlinear equations in Banach spaces. We prove an existence-uniqueness theorem and give a priori error bounds which demonstrates the R-order of the method to be six. Finally, we give some numerical applications to demonstrate our approach.