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Extremal characterizations of reflexive spaces

Part of: Existence theories

Published online by Cambridge University Press:  09 April 2009

Xianfu Wang
Xianfu Wang
Affiliation:
Mathematics, The Irving K. Barber School of Arts and SciencesUBC Okanagan3333 University WayKelowna BC VIV 1V7CanadaShawn.Wang@ubc.ca
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Abstract

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Assume that a Banach space has a Fréchet differentiable and locally uniformly convex norm. We show that the reflexive property of the Banach space is not only sufficient, but also a necessary condition for the fulfillment of the proximal extremal principle in nonsmooth analysis.

Keywords

subgradientsproximal extremal principleproximal fuzzy sum rulereflexive space.

MSC classification

Secondary: 49J52: Nonsmooth analysis
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 82 , Issue 3 , June 2007 , pp. 429 - 440
Copyright
Copyright © Australian Mathematical Society 2007

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