  In this paper we provide further studies of the Fenchel duality theory in the
general frame work of locally convex topological vector (LCTV) spaces. We prove
the validity of the Fenchel strong duality under some qualification conditions
via generalized relative interiors imposed on the epigraphs and the domains of
the functions involved. Our results directly generalize the classical
Fenchel-Rockafellar theorem on strong duality from finite dimensions to LCTV
spaces.

Functional Analysis;Optimization and Control