Differentiability of cone-monotone functions on separable Banach space

Title: Differentiability of cone-monotone functions on separable Banach space
Creator: Borwein, Jonathan M.; Burke, James V.; Lewis, Adrian S.
Relation: Proceedings of the American Mathematical Society Vol. 132, Issue 4, p. 1067-1076
Relation: http://www.ams.org/journals/proc/2004-132-04/S0002-9939-03-07149-1/home.html
Publisher: American Mathematical Society
Resource Type: journal article
Date: 2004
Description: 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.
Subject: Lipschitz functions; Gâteaux differentiability; Banach spaces; convex cone
Identifier: uon:6464
Identifier: http://hdl.handle.net/1959.13/803646
Identifier: ISSN:0002-9939
Rights: First published in Proceedings of the American Mathematical Society in Vol. 132, Issue 4, p. 1067-1076, 2004 published by the American Mathematical Society
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