Generalizations of EE-convex and B-vex functions

A class of functions called EE-B-vex functions is defined as a generalization of EE-convex and B-vex functions. Similarly, a class of EE-B-preinvex functions, which are generalizations of EE-convex and B-preinvex functions, is introduced. In addition, the concept of B-linear functions is also generalized to EE-B-linear functions. Some properties of these proposed classes are studied. Furthermore, the equivalence between the class of EE-B-vex functions and that of EE-quasiconvex functions is proved.