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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.

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.

In this paper, we unify the theory of SSD spaces and the theory of strongly representable sets, and we apply our results to the theory of the various classes of maximally monotone sets. In particular, we prove that type (ED), dense type, type (D), type (NI) and strongly representable are equivalent concepts and, consequently, that the known properties of strongly representable sets follow from known properties of sets of type (ED). © Heldermann Verlag.

In this paper, we unify the theory of SSD spaces and the theory of strongly representable sets, and we apply our results to the theory of the various classes of maximally monotone sets. In particular, we prove that type (ED), dense type, type (D), type (NI) and strongly representable are equivalent concepts and, consequently, that the known properties of strongly representable sets follow from known properties of sets of type (ED). © Heldermann Verlag.

In this paper, we show how convex analysis can be applied to the theory of sets that are "positive" with respect to a continuous quadratic form on a Banach space. Monotone sets can be considered as a special case of positive sets, and we show how our results lead to very efficient proofs of a number of results on monotone sets. One of the key techniques that we use is a generalization of the Fitzpatrick function from monotone set theory to an analogous function for positive sets. © Heldermann Verlag.

In this paper, we show how convex analysis can be applied to the theory of sets that are "positive" with respect to a continuous quadratic form on a Banach space. Monotone sets can be considered as a special case of positive sets, and we show how our results lead to very efficient proofs of a number of results on monotone sets. One of the key techniques that we use is a generalization of the Fitzpatrick function from monotone set theory to an analogous function for positive sets. © Heldermann Verlag.

In this paper, we show how Fitzpatrick functions can be used to obtain various results on the local boundedness, domain and surjectivity of monotone and maximal monotone multifunctions on a Banach space, and also to clarify the relationships between different subclasses of the set of maximal monotone multifunctions. © Heldermann Verlag.

In this paper, we show how Fitzpatrick functions can be used to obtain various results on the local boundedness, domain and surjectivity of monotone and maximal monotone multifunctions on a Banach space, and also to clarify the relationships between different subclasses of the set of maximal monotone multifunctions. © Heldermann Verlag.