多元α-预不变凸函数的Hermite-Hadamard型积分不等式  

Integral Inequality of Hermite-Hadamard Type for Multivariate α-preinvex Functions

作　　者：王海英 符祖峰 李婧[1] 谭冰[1] WANG Haiying;FU Zufeng;LI Jing;TAN Bing(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：《湖北民族大学学报（自然科学版）》2023年第2期246-251,共6页Journal of Hubei Minzu University:Natural Science Edition

基　　金：国家自然科学基金项目(41876219);南阳师范学院校级自然科学类科研项目(2022ZX022,2022QN014)。

摘　　要：论文研究了α-预不变凸函数的Hermite-Hadamard型积分不等式。利用Holder不等式、幂平均不等式和函数的α-预不变凸性,对此类广义凸函数的Hermite-Hadamard型积分不等式的左右两边分别给出估计值。借助多元α-预不变凸函数与单变量凸函数之间的关系,将此类函数的Hermite-Hadamard型不等式结果进行推广,得到了多元α-预不变凸函数的2个Hermite-Hadamard型积分不等式。In this paper,we study the Hermite-Hadamard type inequality ofα-preinvex functions.Firstly,by using the Holder inequality,the power mean inequality and theα-preinvexity,we present the estimates of the left and right sides of integral inequality of the Hermite-Hadamard type for such generalized convex functions are presented respectively.Then,by using the relationship between multivariateα-preinvex functions and univariate convex functions,we obtain two inequalities of the Hermite-Hadamard type for functions with several variables.

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

分 类 号：O175.5[理学—数学]