Generalization of B-Preinvex Function and Its Application

A class of generalized convex functions called Bp-vex function is defined by relaxing the definitions of preinvex, B-preinvex and B-vex functions. Examples are given to show that there exist functions which are Bp-vex function but not preinvex or B-vex function or B-preinvex. Some characteristic properties and operational properties of this kind of function are derived, these properties show that the new generalized convex functions in this paper preserve some of the valuable properties of convex functions, so it is necessary to define these generalized convex functions, and it is important to study the application of these generalized convex functions in mathematical programming. Some of its application results in nonlinear programming problem are established finally in the sequel of our discussion, these results obtained not only extend some of the present researches, but also can be apply to the questions occur in economics, engineering, management science and other applied sciences etc. Theoretically, these results are very useful in nonlinear mathematical programming and are helpful to studying generalized convex function. At the same time, using these results, the dual models of some kinds of programs can also be inspected.