In this paper, we present meanings of K-Gf-bonvexity/K-Gf-pseudobonvexity and their generalization between the above-notice functions. We also construct various concrete non-trivial examples for existing these types formulate K-Gf-Wolfe type multiobjective second-order symmetric duality model with cone objective as well constraints theorems have been established under aforesaid conditions. Furt...