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

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.