Miruna Beldiman

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.

On Variational-like Inequalities with Generalized Monotone Mappings

We consider two new classes of generalized relaxed α-monotone and semimonotone functions and using the KKM technique we prove the existence of solutions for variational-like inequalities relative to these types of mappings in Banach spaces. Several examples and special cases are also considered.

On a general duality model in multiobjective fractional programming with n-set functions

We consider some types of generalized convexity and discuss duality results for a fractional programming problem involving (F,b,@f,@r,@q)-univex n-set functions. Almost all results presented until now in the literature were obtained under the assumption that the function F is sublinear or, in the last time, convex in the third argument. In our approach, we suppose that F is a quasiconvex function in the third argument.