The application of an inverse-free Jarratt-type approximation to nonlinear integral equations of Hammerstein-type

We consider an inverse-free Jarratt-type approximation, whose order of convergence is four, for solving nonlinear equations. The convergence of this method is analysed under two different types of conditions. We use a new technique based on constructing a system of real sequences. Finally, this method is applied to the study of Hammersteinʹs integral equations.