Optimality conditions for multiple objective fractional subset programming with (, ρ,σ,θ )-V-type-I and related non-convex functions

In this paper, we introduce a new class of generalized convex n -set functions, called (, ρ,σ,θ)-V-Type-I and related non-convex functions, and then establish a number of parametric and semi-parametric sufficient optimality conditions for the primal problem under the aforesaid assumptions. This work partially extends an earlier work of [G.J. Zalmai, Efficiency conditions and duality models for multiobjective fractional subset programming problems with generalized (, α , ρ , θ )-V-convex functions, Comput. Math. Appl. 43 (2002) 1489–1520] to a wider class of functions.