Sufficiency and duality for multiobjective variational control problems with generalized (F,α,ρ,θ)(F,α,ρ,θ)-V-convexity

Zalmai introduced generalized (F,α,ρ,θ)(F,α,ρ,θ)-V-convex functions, a new class of functions that unifies several concepts of generalized convex functions. In this article, the generalized (F,α,ρ,θ)(F,α,ρ,θ)-V-convex functions are extended to variational control problem. By utilizing the new concepts, we obtain sufficient optimality conditions and prove Wolfe type and Mond–Weir type duality results for multiobjective variational control programming problem.