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A Fixed Point Theorem and an Application to Bellman Operators
Graduate School of Economics, Keio University, Tokyo, Japan
Graduate School of Economics, Keio University, Tokyo, Japan
- 1 Graduate School of Economics, Keio University, Tokyo, Japan
- 2 Graduate School of Economics, Keio University, Tokyo, Japan
Theoretical Economics Letters·Volume 03 (2013)·Pages 65–68·Published 26 February 2013·DOI10.4236/tel.2013.31010
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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.
KeywordsBellman OperatorUniform Convergence
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