On Newton-kantorovich method for solving the nonlinear operator equation

We develop the Newton-Kantorovich method to solve the system of 2 × 2 nonlinear Volterra integral equations where the unknown function is in logarithmic form. A new majorant function is introduced which leads to the increment of the convergence interval. The existence and uniqueness of approximate solution are proved and a numerical example is provided to show the validation of the method.