Generalized V-univexity type-I for multiobjective programming with n-set functions

In the last time important results in multiobjective programming involving type-I functions were obtained (Yuan et al. in: Konnov et al. (eds) Lecture notes in economics and mathematical systems, 2007; Mishra et al. An Univ Bucureşti Ser Mat, LII(2): 207–224, 2003). Following one of these ways, we study optimality conditions and generalized Mond-Weir duality for multiobjective programming involving n -set functions which satisfy appropriate generalized univexity V-type-I conditions. We introduce classes of functions called ( ρ , ρ ′)-V-univex type-I, ( ρ , ρ ′)-quasi V-univex type-I, ( ρ , ρ ′)-pseudo V-univex type-I, ( ρ , ρ ′)-quasi pseudo V-univex type-I, and ( ρ , ρ ′)-pseudo quasi V-univex type-I. Finally, a general frame for constructing functions of these classes is considered.