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Epi-Lipschitz-like sets in Banach space: theorems and examples

Borwein, Jonathan M. (1987) Epi-Lipschitz-like sets in Banach space: theorems and examples. Nonlinear Analysis: Theory, Methods and Applications, 11 . pp. 1207-1217.

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Abstract

One can, following Rockafellar, define generalized derivatives of arbitrary functions on arbitrary topological vector spaces. In this generality, only a few relatively unrefined results can be established. These results typically do not recapture much of the detailed information available in Rn or for Lipschitz functions. To obtain more delicate results it is necessary to restrict either the spaces or the functions. Many examples are available in Borwein and Strojwas which illustrate how badly wrong things may go outside of a Baire metrizable or Banach space setting. In this paper we restrict our attention primarily to a Banach space X and consider what properties a set C in X should have for the Clarke tangent cone Tc(x) and normal cone Nc(x) to adequately measure boundary behaviour of x in C.

Item Type: Article
Subjects: UNSPECIFIED
Faculty: UNSPECIFIED
Depositing User: Mrs Naghmana Tehseen
Date Deposited: 20 Feb 2015 16:20
Last Modified: 20 Feb 2015 16:20
URI: https://docserver.carma.newcastle.edu.au/id/eprint/1599

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