FIXED POINT THEOREMS FOR DISCONTINUOUSMAPPINGSLudwig
نویسندگان
چکیده
We prove a generalization of Brouwer's famous xed point theorem to discontinuous maps. The main result shows that for discontinuous functions on a compact convex domain X one can always nd a point x 2 X such that kx ? f(x)k is less than a certain measure of discontinuity. Applications to artiicial neural nets, economic equilibria, and analysis are given.
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