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Fixed Point Theorems

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The New Palgrave Dictionary of Economics

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Abstract

This article gives statements of the Tarski fixed point theorem and the main versions of the topological fixed point principle that have been applied in economic theory. Pointers are given to literature concerned with proofs of Brouwer’s theorem, and with algorithms for computing approximate fixed points. The topological results are all consequences of a slightly weakened version of the Eilenberg and Montgomery (American Journal of Mathematics 68: 214–222, 1946) fixed point theorem. The axiomatic characterization of the Leray–Schauder fixed point index (which is even more powerful) is also stated, and its application to issues concerning robustness of sets of equilibria is explained.

This chapter was originally published in The New Palgrave Dictionary of Economics, 2nd edition, 2008. Edited by Steven N. Durlauf and Lawrence E. Blume

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  1. http://link.springer.com/referencework/10.1057/978-1-349-95121-5

    Andrew McLennan

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    McLennan, A. (2008). Fixed Point Theorems. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95121-5_646-2

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    • DOI: https://doi.org/10.1057/978-1-349-95121-5_646-2

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    • Online ISBN: 978-1-349-95121-5

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    Chapter history

    1. Latest

      Fixed Point Theorems
      Published:
      19 April 2017

      DOI: https://doi.org/10.1057/978-1-349-95121-5_646-2

    2. Original

      Fixed Point Theorems
      Published:
      11 November 2016

      DOI: https://doi.org/10.1057/978-1-349-95121-5_646-1