Fenchel–Rockafellar theorem in infinite dimensions via generalized relative interiors

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