Location, separation and approximation of solutions of nonlinear Hammerstein-type integral equations

Abstract

From Newton's method, we construct a Newton-type iterative method that allows studying a class of nonlinear Hammerstein-type integral equations. This method is reduced to Newton's method if the kernel of the integral equation is separable and, unlike Newton's method, can be applied to approximate a solution if the kernel is nonseparable. In addition, from an analysis of the global convergence of the method, we can locate and separate solutions of the nonlinear Hammerstein-type integral equations involved. For this study of the global convergence, we use auxiliary functions and obtain restricted global convergence domains that are usually balls.