Semilocal convergence of a modified multi-point Jarratt method in Banach spaces under general continuity condition (Q438803)

The semilocal convergence for a modified multi-point Jarratt method for solving nonlinear equations in Banach spaces is established with the third-order Fréchet derivative of the operator under a general continuity condition. The recurrence relations are derived for the method, and from this, an existence-uniqueness theorem is proved, and a priori error bounds are determined. The \(R\)-order of the method is also analyzed with the third-order Fréchet derivative of the operator under different continuity conditions. A numerical application on a nonlinear integral equation of mixed type is given, too.