Existence and Uniqueness of a Fixed Point for Local Contractions

V. Filipe Martins-da-Rocha, Yiannis Vailakis

Econometrica · 2010 · Volume 78 · Issue 3

Abstract

This paper proves the existence and uniqueness of a fixed point for local contractions without assuming the family of contraction coefficients to be uniformly bounded away from 1. More importantly it shows how this fixed-point result can apply to study the existence and uniqueness of solutions to some recursive equations that arise in economic dynamics.

Keywords

Fixed-point theorem, local contraction, Bellman operator, Koopmans operator, Thompson aggregator, recursive utility

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