In this paper, a new class of second-order (F, α, ρ, d)-V-type I functions is introduced that generalizes the notion of (F, α, ρ, θ)-V-convex functions introduced by Zalmai (Computers Math. Appl. 2002; 43:1489–1520) and (F, α, ρ, p, d)-type I functions defined by Hachimi and Aghezzaf (Numer. Funct. Anal. Optim. 2004; 25:725–736). Based on these functions, weak, strong, and strict converse duality theorems are derived for Wolfe and Mond–Weir type multiobjective dual programs in order to relate the efficient and weak efficient solutions of primal and dual problems.