# Cone monotone functions: differentiability and continuity

Borwein, Jonathan M. and Wang, Shawn Xianfu (2005) Cone monotone functions: differentiability and continuity. Canadian J. Math, 57 . pp. 961-982.

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We provide a porosity notion approach to the differentiability and continuity of real valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone $K$ with non-empty interior. We also show that the set of nowhere $K$-monotone functions has a $\sigma$-porous complement in the space of the continuous functions.