Displaying similar documents to “Examples of convex functions and classifications of normed spaces.”

Stability of Supporting and Exposing Elements of Convex Sets in Banach Spaces

Azé, D., Lucchetti, R. (1996)

Serdica Mathematical Journal

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* This work was supported by the CNR while the author was visiting the University of Milan. To a convex set in a Banach space we associate a convex function (the separating function), whose subdifferential provides useful information on the nature of the supporting and exposed points of the convex set. These points are shown to be also connected to the solutions of a minimization problem involving the separating function. We investigate some relevant properties of this function...

Stability results for convergence of convex sets and functions in nonreflexive spaces.

Jaafar Lahrache (1996)

Publicacions Matemàtiques

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Let Γ(X) be the convex proper lower semicontinuous functions on a normed linear space X. We show, subject to Rockafellar’s constraints qualifications, that the operations of sum, episum and restriction are continuous with respect to the slice topology that reduces to the topology of Mosco convergence for reflexive X. We show also when X is complete that the epigraphical difference is continuous. These results are applied to convergence of convex sets.