Nonlinear Fredholm integral equations and majorant functions

From the majorant principle of Kantorovich and the theoretical significance of Newton's method, we obtain domains of existence and uniqueness of solution for nonlinear Fredholm integral equations, so that these domains are defined from the positive real zeros of a scalar function that we call majorant function. We illustrate this study with three Fredholm integral equations, where separable and nonseparable kernels are involved, by obtaining domains of existence and uniqueness of solution, approximating solutions numerically and giving a priori and a posteriori error estimates of the approximations.