ABSTRACT
The convexity theory plays an important role in many aspects of mathematical programming. In recent years, in order to relax convexity assumption, various generalized convexity notions have been obtained. One of them is the concept of B− (p, r) invexity defined by T. Antczak [1], which extended the class of B-invex functions with respect to η and b and the classes of (p, r)-invex functions with respect to η [2][3]. He proved some necessary and sufficient conditions for B− (p, r)-invexity and showed the relationships between the defined classes of B− (p, r)-invex functions and other classes of invex functions. Later Antczak defined a classes of generalized invex functions [4], that is B− (p, r)- pseudo-invex functions, strictly B− (p, r) pseudoinvex functions, and B− (p, r)-quasi-invex functions, considered single objective mathematical programming problem involvingB− (p, r)-pseudo-invex functions, B− (p, r)-quasi-invex functions and obtained some sufficient optimality conditions, Zengkun xu [5] considered multiobjective programming problems by a class of generalized (F , ρ) convex functions, studied mixed type dual, derived many weak, strong, strictly reverse dual conditions, Mohamed Hachimi, Brahim Aghezzaf [6] defined generalized (F , α, ρ, d)- type functions, considered multiobjective program by (F , α, ρ, d)-type functions, derived many dual conditions Xiangyou Li [7] discussed saddle-point conditions for multi-objective programming.
