A Fixed Point Theorem and an Application to Bellman Operators

Yuhki Hosoya, Masayuki Yao

Graduate School of Economics, Keio University, Tokyo, Japan.

DOI: 10.4236/tel.[phone]                

Abstract

This study introduces a new definition of a metric that corresponds with the topology of uniform convergence on any compact set, and shows both the existence of a unique fixed point of some operator by using this metric and that the iteration of such an operator results in convergence to this fixed point. We demonstrate that this result can be applied to Bellman operators in many situations involving economic dynamics.

Keywords

Bellman Operator; Uniform Convergence

Conflicts of Interest

The authors declare no conflicts of interest.

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