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A note on a theorem of F. Browder

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Abstract

A particular case of a mathematical theorem of F. Browder on the behavior of the fixed point set of a mapping under variations of a parameter has recently found applications in programming theory in connection with the abstract (non-linear) complementarity problem (see Eaves, [2, 3]). Two relevant extensions of Browder's result are provided: The first asserts that, under smoothness assumptions, the connected set of fixed points one gets from Browder's theorem is “generically” an arc; the second gives a generalization to the case where the mapping is an upper hemicontinuous contractible valued correspondence.

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References

  1. F. Browder, “On continuity of fixed points under deformation of continuous mappings”,Summa Brasiliensis Mathematicae 4 (1960).

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Authors and Affiliations

  1. University of California, Berkeley, California, USA

    Andreu Mas-Colell

Authors
  1. Andreu Mas-Colell
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Additional information

Research for this work has been supported by N.S.F. Grants G.S.-27226 and G.S.-3274.

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Mas-Colell, A. A note on a theorem of F. Browder. Mathematical Programming 6, 229–233 (1974). https://doi.org/10.1007/BF01580239

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  • DOI: https://doi.org/10.1007/BF01580239

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