对数η-凸函数的积分不等式  

Integral Inequalities for Log-η-Convex Functions

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

机构地区：[1]海军指挥学院信息系,南京211800

出　　处：《湖南理工学院学报（自然科学版）》2017年第3期1-5,共5页Journal of Hunan Institute of Science and Technology(Natural Sciences)

摘　　要：对数η-凸函数是对数凸函数的推广,对数η-凸函数积分不等式的研究可以从对数凸函数积分不等式的研究中得到启示.从对数η-凸函数的定义出发,结合一些分析技巧,建立了涉及对数η-凸函数的积分不等式,得到其算术平均值的上下界.在特殊情况下得到对数凸函数的Hermite-Hadamard型不等式.Log-η-convex functions are the generalization of log-convex functions. The study of integral inequalities for log-η-convex functions can be inspired from the study of integral inequalities for log-convex functions. Based on the definition of log-η-convex functions and using some analytic skills, the integral inequalities are established, and the upper and lower bounds of the arithmetic mean involving log-η-convex functions are obtained. In particular cases, Hermite-Hadamard type inequalities for log-convex functions are obtained.

关 键 词：对数η-凸函数 对数凸函数 积分不等式 

分 类 号：O178[理学—数学] O174.13[理学—基础数学]