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Differentiability of cone-monotone functions on separable Banach space

Borwein, Jonathan M. and Burke, James V. and Lewis, Adrian (2004) Differentiability of cone-monotone functions on separable Banach space. Proceedings of the American Mathematical Society, 132 (4). pp. 1067-1076.

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Abstract

Motivated by applications to (directionally) Lipschitz functions, we provide a general result on the almost everywhere Gâteaux differentiability of real-valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone with nonempty interior. This seemingly arduous restriction is useful, since it covers the case of directionally Lipschitz functions, and necessary. We show by way of example that most results fail more generally.

Item Type: Article
Uncontrolled Keywords: Lipschitz functions, Gâteaux differentiability, Banach spaces, convex cone
Subjects: UNSPECIFIED
Faculty: UNSPECIFIED
Depositing User: Dr David Allingham
Date Deposited: 28 Sep 2012 12:05
Last Modified: 09 Sep 2014 12:07
URI: https://docserver.carma.newcastle.edu.au/id/eprint/1242

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