Approximate solutions of Hammerstein's equation in Banach space (Q1070511)

This article deals with Hammerstein equations of the type \(x+BFx=y\) with a monotonic and hemicontinuous operator \(F: X\to X^*\) and a linear monotonic and bounded operator \(B: X^*\to X\), where X is a real strongly convex Banach space and \(X^*\) is a uniformly convex one. The author proves an existence and uniqueness theorem for this equation and describes the behaviour of solutions to regularized (by replacing B with \(B+2U\), U being the dual mapping from \(X^*\) into X) equations, as well as Galerkin approximations. An illustrating example in the case \(X=\ell_ p\) is considered.