A non-convex analogue to Fenchel duality

We introduce and study a new notion of conjugacy, similar to Fenchel conjugacy, in a non-convex setting. Dual versions of Smulyan's classical result are established in the framework of this conjugacy, which reveal a relation between well-posed problems and the differentiability. As an application we deduce the generic Frechet differentiability of the norm parallel to.parallel to (proportional to) in certain spaces of bounded continuous functions (i.e.. Lip(alpha)(X) for 0 < x < 1). (C) 2001 Academic Press.