Iterative solutions of parameter-dependent nonlinear equations of hammerstein type

The unique solution of a general nonlinear Hammerstein-type equation is obtained based on the contraction mapping principle. Introducing a suitable weighted norm, the range of values of the involved parameter allowed by the contraction mapping principle is shown to be increased. Detailed construction of the suitable weight function is given. Application to a specific Hammerstein integral equation is considered supported by a numerical example.