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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/803646

Title

Differentiability of cone-monotone functions on separable Banach space

Author/Creator

Borwein, Jonathan M.;  Burke, James V.;  Lewis, Adrian S.

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.

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

Date

2004

Publisher

American Mathematical Society

Keyword(s)

Lipschitz functions;  Gâteaux differentiability;  Banach spaces;  convex cone

Resource Type

journal article

Identifier

http://hdl.handle.net/1959.13/803646

Identifier

ISSN:0002-9939

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Subject

"Proceedings of the American Mathematical Society"

 

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