Semilocal convergence of a multipoint fourth-order super-Halley method in Banach spaces

In this paper, we study a variant of the super-Halley method with fourth-order convergence for nonlinear equations in Banach spaces. We make an attempt to establish the semilocal convergence of this method by using recurrence relations. The recurrence relations for the method are derived and then an existence-uniqueness theorem is given to establish the R-order of the method to be four and a priori error bounds. Finally, some numerical applications are presented to demonstrate our approach.