Fixed point theorems for discontinuous mapping

Fixed point theorems for discontinuous mapping

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Article ID: iaor1993316
Country: Netherlands
Volume: 51
Issue: 2
Start Page Number: 257
End Page Number: 267
Publication Date: Sep 1991
Journal: Mathematical Programming (Series A)
Authors: ,
Abstract:

The authors prove a genrealization of Brouwer’s famous fixed point theorem to discontinuous maps. The main result shows that for discontinuous functions on a compact convex domain X one can always find a point x∈X such that ∈x-f(x)∈ is less than a certain measure of discontinuity. Applications to artificial neural nets, economic equilibria and analysis are given.

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