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Journal of Convex Analysis 13 (2006), No. 3, 751--758
Copyright Heldermann Verlag 2006

Differentiability of Lipschitz Functions on a Space with Uniformly Gâteaux Differentiable Norm

John Robilliard Giles
School of Mathematical and Physical Sciences, University of Newcastle, Newcastle, NSW 2305, Australia

On a normed linear space with uniformly Gâteaux differentiable norm a locally Lipschitz function which satisfies a property relating the Dini derivatives to a constant determined by the Michel-Penot derivative possesses significant differentiability properties. This generalises previous joint work with Simon Fitzpatrick.

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