Second order symmetric duality with generalized convexity

Two distinct pairs of second order symmetric dual programs are considered and appropriate duality theorems are established under η1-convexity/η2-concavity and η1-pseudoconvexity/η2-pseudoconcavity of the kernel function K(x,y). Assuming the additional hypothesis of skew symmetry for K(x,y) these programs are shown to be self dual. Also, it is observed that for a particular kernel function, both these pairs are reduced to the general nonlinear problem and its Wolfe type second order dual introduced by Mangasarian.