N次幂下S-凸函数和其性质研究  

Research on s-convex functions and its properties under n-th power

作　　者：刘明术 方宏彬[2] LIU Mingshu;FANG Hongbin(Huangshan Vocational and Technical College,Huangshan,Anhui 245000;School of Mathmatics and Computational Science,Anhui university,Hefei 230039)

机构地区：[1]黄山职业技术学院,安徽黄山245000 [2]安徽大学数学与计算科学学院,安徽合肥230039

出　　处：《池州学院学报》2024年第3期6-9,共4页Journal of Chizhou University

摘　　要：以凸函数、S-凸函数、平方凸函数、平方S-凸函数的定义和性质为研究基础,根据从平方凸函数到平方S-凸函数的演变推进过程,采用了凸函数概念的代数不等式形式,给出了N次幂下S-凸函数的概念,并对其判别定理和性质进行了讨论,定义并证明了N次幂下S-凸函数的Jensen型不等式。研究表明,N次幂下S-凸函数包含了凸函数、平方凸函数、平方S-凸函数的性质,是凸函数的一种广义凸函数的推广,开辟了全新的推广途径。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 sconvex 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.

关 键 词：JENSEN不等式 S-凸函数 平方凸函数 平方S-凸函数 判别定理 

分 类 号：O178.1[理学—数学]