A fixed point theorem for discontinuous functions

P.J.J. Herings; G. van der Laan; A.J.J. Talman; Z. Yang

doi:10.1016/j.orl.2007.03.008

A fixed point theorem for discontinuous functions

P.J.J. Herings
, G. van der Laan
, A.J.J. Talman
, Z. Yang

Research output: Contribution to Journal › Article › Academic › peer-review

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. © 2007 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	89-93
Journal	Operations Research Letters
Volume	36
DOIs	https://doi.org/10.1016/j.orl.2007.03.008
Publication status	Published - 2008

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title = "A fixed point theorem for discontinuous functions",

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. {\textcopyright} 2007 Elsevier B.V. All rights reserved.",

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AU - Talman, A.J.J.

AU - Yang, Z.

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AB - 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. © 2007 Elsevier B.V. All rights reserved.

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SN - 0167-6377

VL - 36

SP - 89

EP - 93

JO - Operations Research Letters

JF - Operations Research Letters

ER -

A fixed point theorem for discontinuous functions

Abstract

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