E-预不变凸函数的Hermite-Hadamard型积分不等式及应用  

Hermite-Hadamard type integral inequality for E-preinvex functions and its application

作　　者：王海英 符祖峰 高景利[1] 虎大力 WANG Haiying;FU Zufeng;GAO Jingli;HU Dali(School of Mathematics and Statistics,Nanyang Normal University,Nanyang 473061,China)

机构地区：[1]南阳师范学院数学与统计学院,河南南阳473061

出　　处：《南阳师范学院学报》2023年第6期22-28,共7页Journal of Nanyang Normal University

基　　金：国家自然科学基金项目(61801250);南阳师范学院校级自然科学类科研项目(2022ZX022,2022QN014)。

摘　　要：建立了E-预不变凸函数的Hermite-Hadamard型积分不等式。首先,利用分部积分法和变量代换,建立了E-预不变凸函数的Hermite-Hadamard型积分不等式。其次,利用Holder不等式、幂平均不等式和函数的E-预不变凸性,对获得的此类广义凸函数的Hermite-Hadamard型积分不等式的左右两边的不等式分别给出估计值。接着,利用多元E-预不变凸函数与单变量凸函数之间的关系,将建立的Hermite-Hadamard型不等式结果进行推广,得到了多元E-预不变凸函数的两个Hermite-Hadamard型积分不等式。最后,给出了E-预不变凸函数的Hermite-Hadamard型积分不等式在一些特殊均值上的应用。In this paper,the Hermite-Hadamard type inequality for E-preinvex functions is established.Firstly,the Hermite-Hadamard type integral inequalities for E-preinvex functions are established by using the partial integration method and variable substitution.Secondly,the estimates of the left and right sides of the Hermite-Hamard type integral inequalities for such generalized convex functions are presented respectively using the Holder inequality,the power mean inequality and the E-preinvexity.And then,by using the relationship between multivariate E-preinvex functions and univariate convex functions,two results of the Hermite-Hadamard type inequality for functions with several variables are obtained.Finally,some applications of the Hermite-Hadamard type inequality to special means are also provided.

关 键 词：E-预不变凸函数 Hermite-Hadamard型积分不等式 HOLDER不等式 幂平均不等式 

分 类 号：O221.1[理学—运筹学与控制论]