Semilocal convergence of a class of modified super-Halley methods in Banach spaces (Q438773)

The authors consider the semilocal convergence of a class of modified super-Halley methods for solving nonlinear equations in Banach spaces. The semilocal convergence of this class of methods is established by using recurrence relations. A system of recurrence relations for the methods is constructed, and based on it, an existence-uniqueness theorem that shows the \(R\)-order of the methods is proved.