Decomposition methods: A new proof of convergence (Q1324723)

The authors consider nonlinear equations of the form (*) \(u-N(u)=f\) where \(N\) and \(f\), respectively, are operator and function given in convenient spaces. They construct a solution of (*) in the form (+) \(u=\sum^ \infty_{i=0} u_ i\) where the \(u_ i\) are successively defined. A convergence proof of the series (+) is proposed and the error of the truncated series of (+) is estimated. No application is given. [Remark: The proof is not very distinct; in particular, the space in which the proof is valid is not stated].