Iterative solutions for systems of nonlinear operator equations in Banach space (Q1418257)

On a real Banach space with a partial ordering induced by a normal cone, the author considers a system of nonlinear equations of the form (1) \(u = A(u,u), u = B(u,u)\) under a particular set of assumptions for the operators \(A\) and \(B\) that do not require them to be mixed monotone or continuous. The convergence of a specific iterative scheme is proved and related results for the existence and uniqueness of solutions of (1) are discussed.