广义凸函数及其应用  

Generalized Convex Function and Its Applications

作　　者：江慎铭[1] 

机构地区：[1]南昌航空大学,江西南昌330063

出　　处：《南昌航空大学学报（自然科学版）》2011年第1期67-70,共4页Journal of Nanchang Hangkong University(Natural Sciences)

基　　金：南昌航空大学教改课题项目(JY0974)

摘　　要：文章类比凸函数引进广义凸函数的概念,并给出了两个判定广义凸函数的方法,其中微分判别法是一种实用而有效的判定方法。通过这个判定方法建立关于广义凸函数的不等式,其形式上类似于凸函数的Jensen不等式,并利用它推广一些已有的不等式。In this paper,concept of generalized convex function which is similar to that of convex function is defined.Two criteria of the concept are given.In particular,the differential criterion is efficient and practical.Moreover,the inequality for generalized convex function is given by the criteria,which has the form similar to the famous Jensen inequality for convex functions.By using the inequality,some old ones are generalized.

关 键 词：广义凸函数 JENSEN不等式 不等式 

分 类 号：O178[理学—数学]