Second and higher order duality in Banach space under ρ−(η,θ)ρ−(η,θ)-invexity

In this paper, we introduce the concept of second and higher order duality in Banach space using ρ−(η,θ)ρ−(η,θ)-invexity type conditions. Duality theorems for Mangasarian type, Mond–Weir type are established under weaker conditions. We also give counter examples to justify our work.