积分型Kantorovich不等式注记  

Remarks on Kantorovich Integral Inequality

作　　者：时统业[1] 秦华[1] SHI Tongye;QIN Hua(Department of Information,PLA Naval Command College,Nanjing 211800,PRC)

机构地区：[1]海军指挥学院信息系,江苏南京211800

出　　处：《高等数学研究》2018年第4期10-14,共5页Studies in College Mathematics

摘　　要：针对具有凸性或单调增加的函数f,研究积分型的Kantorovich不等式.在f和1/f均为正值的凸函数的条件下,给出积分型的Kantorovich不等式右边部分的一个改进.在f同时为正值的凸函数和对数凹函数的条件下,给出积分型的Kantorovich不等式左边部分的一个加细.另外,在f为正的单调增加函数的情况下,给出Kantorovich不等式右边部分的一个加细.For convex or monotonically increasing function f,Kantorovich integral inequality is studied.Under the condition that both f and 1/f are positive convex,an improvement of the right-hand side of Kantorovich integral inequality is given.A refinement of the left-hand side of Kantorovich integral inequality is given under the condition that fis both positive convex and logarithmic concave.In addition,a refinement of the right-hand side of Kantorovich integral inequality is obtained when fis positive and monotonically increasing.

关 键 词：积分型Kantorovich不等式 凸函数 单调增加函数 

分 类 号：O174.13[理学—数学] O178[理学—基础数学]