An odd theorem

Eaves, B. Curtis

doi:10.1090/S0002-9939-1970-0270757-2

An odd theorem

Author: B. Curtis Eaves
Journal: Proc. Amer. Math. Soc. 26 (1970), 509-513
MSC: Primary 90.60
DOI: https://doi.org/10.1090/S0002-9939-1970-0270757-2
MathSciNet review: 0270757
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Abstract: Let $C$ be a bounded convex polyhedral set and let $f:C \to C$ be continuous and piecewise linear. Using notions from complementary pivot theory, it is shown that if each fixed point of $f$ lies interior to some piece of linearity, then $f$ has an odd number of fixed points. In addition, an algorithm is given for computing a fixed point of $f$.

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