Decomposition methods: A new proof of convergence.

*(English)*Zbl 0805.65057The authors consider nonlinear equations of the form (*) $u-N\left(u\right)=f$ where $N$ and $f$, respectively, are operator and function given in convenient spaces. They construct a solution of (*) in the form (+) $u={\sum}_{i=0}^{\infty}{u}_{i}$ 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].

Reviewer: W.Petry (Düsseldorf)