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A Fixed Point Theorem and an Application to Bellman Operators

Author

Listed:
  • Yuhki Hosoya

    (Graduate School of Economics, Keio University)

  • Masayuki Yao

    (Graduate School of Economics, Keio University)

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.

Suggested Citation

  • Yuhki Hosoya & Masayuki Yao, 2013. "A Fixed Point Theorem and an Application to Bellman Operators," Keio/Kyoto Joint Global COE Discussion Paper Series 2012-025, Keio/Kyoto Joint Global COE Program.
    • Handle: RePEc:kei:dpaper:2012-025
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    File URL: https://ies.keio.ac.jp/old_project/old/gcoe-econbus/pdf/dp/DP2012-025.pdf
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    References listed on IDEAS

    as
    1. Takashi Kamihigashi, 2014. "Elementary results on solutions to the bellman equation of dynamic programming: existence, uniqueness, and convergence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 251-273, June.
    2. Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), 2006. "Handbook on Optimal Growth 1," Springer Books, Springer, number 978-3-540-32310-5, December.
    3. Cuong Le Van, 2006. "Optimal Growth Models with Discounted Return," Springer Books, in: Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), Handbook on Optimal Growth 1, chapter 2, pages 19-54, Springer.
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