Some results on Fenchel-Rockafellar type of duality and applications

Some of the Fenchel-Rockafellar type of duality theorems derived by Kanniappan are extended for the optimization problems involving set functions. The main tools are derived from the extended concepts of convex set functions by it’s epigraph along with proper definition of W*-semicontinuity of set functions as defined by Chou, Hsia and Lee. Kanniappan’s Lagrangian methods are also used in such derivations. Some miscellaneous applications are, further given for Fenchel-Rockafellar type of duality results.