Verallgemeinerte konvexe funktionen1

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Abstract
Several authors generalized the conjugation in the sense of Fenchel so that it is not realized with respect to the (component-wise) continuous bilinear form (x, y) over X × Y (a – dual – topological pair), but that this is replaced by an arbitrary coupling functional ϕ ∊ R X × Y . Properties of such functionals j have been studied, which, by means of a twofold conjugation with respect to ϕ, are transformed into themselves. The aim of this paper is to give a set-theoretic description by means of the epigraph of these functionals, which proves to be equivalent to the analytical one.

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