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

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.