Approximation of solutions of nonlinear integral equations of Hammerstein type (Q429064)

Summary: Suppose that \(H\) is a real Hilbert space and \(F, K : H \rightarrow H\) are bounded monotone maps with \(D(K) = D(F) = H\). Let \(u^\ast\) denote a solution of the Hammerstein equation \(u + KFu = 0\). An explicit \textit{iteration process} is shown to converge strongly to \(u^\ast\). No invertibility or continuity assumption is imposed on \(K\) and the operator \(F\) is not restricted to be angle-bounded. Our result is a significant improvement on the Galerkin method of Brézis and Browder.