On Krasnoselskii's cone fixed point theorem.

Kwong, Man Kam

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Maps $f$ defined on the interior of the standard non-negative cone $K$ in $ℝ^{N}$ which are both homogeneous of degree $1$ and order-preserving arise naturally in the study of certain classes of Discrete Event Systems. Such maps are non-expanding in Thompson’s part metric and continuous on the interior of the cone. It follows from more general results presented here that all such maps have a homogeneous order-preserving continuous extension to the whole cone. It follows that the extension must have...