Abstract
Consider a non-empty proper closed subset K of a Banach space $(X, \| \cdot \|)$ where the norm is uniformly Gateaux (uniformly Frechet) differentiable. Then the associated distance function d is guaranteed to be Gateaux differentiable on a dense subset D of X\K. Furthermore, Gateaux (Frechet) differentiability of the distance function at a point $x \in$ X\K can be characterised in terms of the weak* sequences ${d' (x_n)}$ where ${x_n}$ is a sequence in D converging to x.
Information
Published: 1 January 1988
First available in Project Euclid: 18 November 2014
zbMATH: 0673.41036
MathSciNet: MR1009591
Rights: Copyright © 1988, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.