Constantin Zalinescu

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We provide a rule to calculate the subdifferential of the pointwise supremum of an arbitrary family of convex functions defined on a real locally convex topological vector space. Our formula is given exclusively in terms of the data functions, and does not require any assumption either on the index set on which the supremum is taken or on the involved(More)
When dealing with convex functions defined on a normed vector space X the biconjugate is usually considered with respect to the dual system (X, X∗), that is, as a function defined on the initial space X. However, it is of interest to consider also the biconjugate as a function defined on the bidual X∗∗. It is the aim of this note to calculate the(More)
In this paper we study and compare the notions of uniform convexity of functions at a point and on bounded sets with the notions of total convexity at a point and sequential consistency of functions, respectively. We establish connections between these concepts of strict convexity in infinite dimensional settings and use the connections in order to obtain(More)