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Cone-Monotone Functions: Differentiability and Continuity
Published online by Cambridge University Press: 20 November 2018
Abstract
We provide a porosity-based 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 continuous functions endowed with the uniform metric.
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- Research Article
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- Copyright © Canadian Mathematical Society 2005
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