Based on the study of the definitions and properties of convex functions,convex functions,squared convex functions and squared s-convex functions,according to the evolution process from square convex functions to square s-convex function,by using the algebraic inequality form of the concept ofconvex function,the concept of s-convex fuction under the power of N is defined,and its discriminant theorem and related properties are discussed.In this paper,we establish and prove Jensen-type inequalities for s-convex function under N power.It is shown that the s-convex function under the power of N contains the properties of convex function,square convex function and square s-convex function,it opensup a new way for the further study and generalization of convex fuction.
维普
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