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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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    Abstract

    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.

    Item Type: Article
    Additional Information: pubdom FALSE
    Uncontrolled Keywords: Cone-monotone functions, Aronszajn null set, porous sets, Gateaux differentiability, singular functions
    Subjects: 26-xx Real functions > 26Bxx Functions of several variables
    58-xx Global analysis, analysis on manifolds > 58Cxx Calculus on manifolds; nonlinear operators
    Faculty: UNSPECIFIED
    Depositing User: Users 1 not found.
    Date Deposited: 20 Nov 2003
    Last Modified: 12 Jan 2015 14:21
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/34

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