Centered forms and interval operators (Q760761)

Centered forms of a function \(f:{\mathbb{R}}^ n\to {\mathbb{R}}^ m\) are considered. It is then pointed out that the centered and generalized centered forms of the Newton-transformation \(s(x):=x-af(x)\) describe known interval operators which have been introduced for the iteration producing sequences of intervals. This fact implies some conclusions with regard to the existence of a fixpoint or the ''best interval operator''.