Second order duality for the variational problems under ρ−(η,θ)ρ−(η,θ)-invexity

In this paper, we introduce the concept of second order duality for the variational problems using ρ−(η,θ)ρ−(η,θ)-invexity type conditions. Weak, strong and converse duality results of Mangasarian and Mond–Weir type of variational problems are established under ρ−(η,θ)ρ−(η,θ)-invexity assumptions. Many examples and counterexamples are illustrated to justify our work.