Approximation of Solutions of Nonlinear Integral Equations of Hammerstein Type with Lipschitz and Bounded Nonlinear Operators

Let E be a reflexive real Banach space with uniformly Gâteaux differentiable norm and F, K : E→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 (e.g., (Chiume and Djitte, 2012)).