平方凸函数Hermite-Hadamard型不等式的改进  

The Improvement of Hermite-Hadamard Type Inequality for Square Convex Functions

作　　者：时统业[1] 秦华[1] 吴涵[1] SHI Tong-ye;QIN Hua;WU Han(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：《大学数学》2018年第1期70-76,共7页College Mathematics

基　　金：海军指挥学院导师及研究生优质课程资助

摘　　要：利用平方凸函数与凸函数的关系,证明了平方凸函数单侧导数的存在性和单调性,建立了平方凸函数与其单侧导数的不等式关系.在此基础上,给出平方凸函数定积分已有下界的改进和新的下界.给出由平方凸函数Hermite-Hadamard型不等式生成的差值的估计.By using the relationships between square convex functions and convex functions,we prove the existence and monotonicity of unilateral derivative of square convex functions and build the relationships between square convex functions and their unilateral derivative by inequality.On the basis of this,not only the improvement of the integral lower bound of square convex functions but also the new lower bound is obtained.The estimations of the difference generated by Hermite Hadamard type inequality of square convex functions are given.

关 键 词：平方凸函数 Hermite-Hadamard型不等式 单侧导数 

分 类 号：O174.13[理学—数学] O178[理学—基础数学]