Generalizations of E-convex and B-vex functionsI

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