Approximation of solutions of nonlinear integral equations of Hammerstein type with Lipschitz and bounded nonlinear operators (Q1954436)

Summary: Let \(E\) be a reflexive real Banach space with uniformly Gâteaux differentiable norm and \(F\), \(K : E \to E\) be Lipschitz accretive maps with \(D(K) = R(F) = E\). Suppose that the Hammerstein equation \(u + KFU = 0\) has a solution. An explicit iteration method is shown to converge strongly to a solution of the equation. No invertibility assumption is imposed on \(K\) and the operator \(F\) is not restricted to be angle-bounded. Our theorems are significant improvements on important recent results.