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Existence and Uniqueness of a Fixed Point for Local Contractions.

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 so...

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Published in:Econometrica Vol. 78; no. 3; pp. 1127 - 1142
Main Authors: Martins-da-Rocha, V. Filipe, Vailakis, Yiannis
Format: Article
Published: Wiley-Blackwell May 2010
Subjects:
Nonlinear programming
Dynamic programming
Utility theory
Recursive functions
Online Access:View this record in EBSCOhost
Summary: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.