Abstract
Under certain conditions, the contraction mapping fixed point theorem guarantees the convergence of the iterationx i+1=f(x i ) toward a fixed point of the functionf:R n →R n. When an interval extensionF off is used in a similar iteration scheme to obtain a sequence of interval vectors these conditions need not provide convergence to a degenerate interval vector representing the fixed point, even if the width of the initial interval vector is chosen arbitrarily small. We give a sufficient condition on the extensionF in order that the convergence is guaranteed. The centered form of Moore satisfies this condition.
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