Duality between differentiability and rotundity for convex functions

V. I. Averbukh

M. V. Lomonosov Moscow State University

Abstract: We generalize a theorem of Asplund and Rockafellar concerning the duality between the differentiability of a convex function with respect to a system of sets $\mathscript A$ and the $\mathscript A$ rotundity of the conjugate convex function to the case of differentiabilities and rotundities defined by pseudotopologies of a broad class, including pseudotopologies of convergence on systems of filters and their bulblike modifications.

UDC: 513.88

Received: 06.02.1973

 English version: Mathematical Notes, 1974, 15:5, 485–491

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