UC Santa Barbara

We discuss the asjTnmetric sandwich theorem, a generalization of the Hahn-Banach theorem. As appUcations, we derive various results on the existence of linear fanctionals that include bivariate, trivariate and quadrivariate generalizations of the Fenchel duahty theorem. Most of the results are about afhne functions defined on convex subsets of vector spaces, rather than Unear functions defined on vector spaces. We consider both results that use a simple boundedness hypothesis (as in Rockafellar's version of the Fenchel duaUty theorem) and also results that use Baire's theorem (as in the Robinson-Attouch-Brezis version of the Fendiel duaUty theorem). This paper also contams some new results about metrizable topological vector spaces that are not necessarily locally convex. © Heldermann Verlag.