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Quadrivariate existence theorems and strong representability


In this article, we give conditions under which we can compute the conjugate of a convex function on the product of two Fréchet spaces defined in terms of another convex function on the product of two (possibly different) Fréchet spaces. We use this result to give simple proofs of some (both old and new) results for Banach spaces, and deduce some (both old and new) stability results for strongly representable multifunctions. We take as our starting point a result on closed convex cones in the product of two Fréchet spaces. © 2011 Taylor & Francis.

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