Extensions and fixed points of contractive maps in \(\mathbb{R}^ n\) (Q1191646)

This article deals with constructive aspects (within Bishop's constructive mathematics) of the fixed point theory for contractive and nonexpansive mappings on subsets of the finite dimensional space \(R^ m\). The main results are a constructive algorithm for the computation of the fixed point of a contractive self-map of a compact convex subset of \(R^ n\), some results on continuation of a contractive self-map from a compact subset of \(R\) on the whole \(R\), and a corresponding counter example for \(R^ 2\), and some constructive results about the convergence of the sequence of iterates of a bounded contractive self-map of \(R^ 2\).