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When some variational properties force convexity

Published online by Cambridge University Press:  17 May 2013

M. Volle
Department of Mathematics, University of Avignon, France.
J.-B. Hiriart-Urruty
Institut de Mathématiques, Université Paul Sabatier, Toulouse, France;
C. Zălinescu
Faculty of Mathematics, University Al. I. Cuza, Iaşi, Romania Octav Mayer Institute of Mathematics, Romanian Academy, Romania;
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The notion of adequate (resp. strongly adequate) function has been recently introduced to characterize the essentially strictly convex (resp. essentially firmly subdifferentiable) functions among the weakly lower semicontinuous (resp. lower semicontinuous) ones. In this paper we provide various necessary and sufficient conditions in order that the lower semicontinuous hull of an extended real-valued function on a reflexive Banach space is essentially strictly convex. Some new results on nearest (farthest) points are derived from this approach.

Research Article
© EDP Sciences, SMAI, 2013

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