Fixed Point Iterations and Global Stability in Economics

Stability is studied from the point of view of ordinary Picard iteration in a metric space. The Convergence Theorem proved here states that a sequence of Picard iterates converges if the mapping in question is a proper convex combination of a contraction (nonexpansive mapping) and the identity. It is shown by examples how this stability condition is related to other ones; in particular, the Convergence Theorem does not follow from any simple variant of the Shrinking Mapping Theorem.