二阶q_(a)-可微凸函数的Hermite-Hadamard型积分不等式  

Hermite-Hadamard Type Integral Inequalities for Convex Function which is Second-order q_(a)-Differentiable

作　　者：刘晨璇 王淑红[1] LIU Chenxuan;WANG Shuhong(College of Mathematical Sciences,Inner Mongolia Minzu University,Tongliao 028043,China)

机构地区：[1]内蒙古民族大学数学科学学院,内蒙古通辽028043

出　　处：《内蒙古民族大学学报（自然科学版）》2024年第1期49-54,共6页Journal of Inner Mongolia Minzu University：Natural Sciences

基　　金：国家自然科学基金项目(12361013);内蒙古自治区直属高校基本科研业务费项目(GXKY22159);内蒙古自治区高等学校科学与技术项目(NJZY20119);内蒙古民族大学博士科研启动基金项目(BS402)。

摘　　要：基于q_(a)-导数和q_(a)-积分,对二阶q_(a)-可微凸函数的Hermite-Hadamard型积分不等式进行了研究。分析二阶q_(a)-导数的特点,寻找二阶q_(a)-导数和q_(a)-积分之间的联系,建立了二阶q_(a)-可微函数的积分恒等式。利用该积分恒等式和函数的凸性,将被积函数进行巧妙分解,结合三角不等式和Hölder不等式等经典不等式,给出了二阶q_(a)-可微凸函数的Hermite-Hadamard型积分不等式的不同的右端估计。Based on q_(a)-derivative and q_(a)-integral,the Hermite-Hadamardt ype integral inequalities of secondorder q_(a)-differentiable convex function is studied.The characteristics of second-order q_(a)-derivative are analyzed,the relation between second-order q_(a)-derivative and q_(a)-integral is found,and the integral identity of second-order q_(a)-differentiable function is established.By using this integral identity and the convexity of function,the integrand function is decomposed skillfully.Integrating the classical inequalities such as triangle inequality and Hölder in⁃equality,different right estimations of Hermite-Hadamard type integral inequality for second-order q_(a)-differentiable convex function are given.

关 键 词：凸函数 HERMITE-HADAMARD不等式 q_(a)-导数 q_(a)-积分 

分 类 号：O172[理学—数学] O178[理学—基础数学]