A super-Halley type approximation in Banach spaces (Q2778240)

This paper deals with the problem of approximating a locally unique zero of the equation \(F(x)=0\) in a Banach space \(X\), where \(F\) is a nonlinear operator defined on a convex subset \(\Omega\) of \(X\) with values in another Banach space \(Y\). A Newton-like method in an approximation of the super-Halley method is studied. The authors establish a Newton-Kantorovich-type convergence theorem using a new system of recurrence relations, and give an explicit expression for the a priori error bounds of the iteration. A priori error bounds obtained for well known integral equations are analysed.