SEVERAL DIFFERENT DEFINITIONS AND FUNCTIONS OF CONVEX FUNCTION

Convex function is an important kind of function and it is widely used in mathematic programming.Considering the relationship beteen continuity and derivative of convex function and their importance of application in proof of some inequalities,several kind of equal definitions of convex function are given in this paper,Their equality,some relative nature and their application in equalities are also discussed.As convex function from above and convex function from below are also called convex function,convex function discussed in this paper refers to convex function from below.