A fixed point theorem for discontinuous functions

A fixed point theorem for discontinuous functions

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Article ID: iaor2009594
Country: Netherlands
Volume: 36
Issue: 1
Start Page Number: 89
End Page Number: 93
Publication Date: Jan 2008
Journal: Operations Research Letters
Authors: , , ,
Abstract:

Any function from a non-empty polytope into itself that is locally gross direction preserving is shown to have the fixed point property. Brouwer's fixed point theorem for continuous functions is a special case. We discuss the application of the result in the area of non-cooperative game theory.

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