Optimality conditions and duality results in Banach space under ρ − (η, θ)-B-invexity

Abstract

In this paper we introduce the notion of \(\rho -(\eta , \theta )\)-B-invex function and generalized \(\rho -(\eta ,\theta )\)-B-invex function between Banach spaces. By considering these functions, sufficient optimality conditions are obtained for a single objective optimization problem in Banach space. Duality results (i.e. weak duality, strong duality and converse duality of Mond–Weir type and similar to Mixed type duals) are established under \(\rho -(\eta , \theta )\)-B-invexity and weak and strong duality of Mond–Weir type dual are also established under generalized \(\rho -(\eta ,\theta )\)-B-invexity in Banach space.