Vol. 82, No. 2, 1979

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Weak local supportability and applications to approximation

Jonathan Borwein

Vol. 82 (1979), No. 2, 323–338

Perturbed optimization problems are studied using a weaker notion of local supportability than that developed by Ekeland and Lebourg. This weakening allows for a more comprehensive treatment of such problems. In particular we prove that nearest points exist densely for closed relatively weakly compact sets in spaces with locally uniformly convex norms and provide a simplified proof in this framework that a normed space with a Fréchet norm is an Asplund space.

Mathematical Subject Classification 2000
Primary: 46B99
Secondary: 41A25, 58C20, 90C30, 49A27
Received: 30 March 1978
Published: 1 June 1979
Jonathan Borwein
Faculty of Computer Science
Dalhousie University
6050 University Avenue
Halifax NS B3H 1W5