指数凸函数算术平均值下界的改进  

The Improvement of the Lower Bound Estimate of the Arithmetic Mean for Exponential Convex Functions

作　　者：时统业[1] 周国辉[1] SHI Tongye;ZHOU Guohui(Department of Information,PLA Naval Command College,Nanjing 211800,China)

机构地区：[1]海军指挥学院信息系,江苏南京211800

出　　处：《杭州师范大学学报（自然科学版）》2018年第1期108-112,共5页Journal of Hangzhou Normal University(Natural Science Edition)

摘　　要：利用凸函数的性质,证明了指数凸函数单侧导数的存在性,并通过不等式建立了指数凸函数与其单侧导数的联系.在此基础上,获得指数凸函数算术平均值的下界,改进了已有结果.Using the properties of convex functions,the existence of unilateral derivatives of exponential convex functions is proved,and the relation between exponential convex functions and its derivative is established through inequalities.On this basis,the lower bounds of the arithmetic mean for exponential convex functions are obtained,which improve the existing results.

关 键 词：指数凸函数 算术平均值 单侧导数 

分 类 号：O178[理学—数学]