Hermite-Hadamard不等式的一类推广  

A Kind of Generalization for Hermite-Hadamard Inequality

作　　者：包琳娜 王淑红[1] BAO Linna;WANG Shuhong(College of Mathematics Science,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)》2025年第1期7-16,共10页Journal of Inner Mongolia Minzu University:Natural Sciences Edition

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)。

摘　　要：基于Katugampola分数阶积分和对数积分,对Hermite-Hadamard不等式进行了加细和推广。引进了二元函数的Katugampola分数阶积分的定义,并分别利用一元函数的凸性和二元函数的协同凸性,建立了一类Hermite-Hadamard型不等式。当取特殊函数时,分别得到了一元凸函数和二元协同凸函数的Hermite-Hadamard不等式、Hermite-Hadamard型分数阶积分不等式和Hermite-Hadamard型对数积分不等式。Based on Katugampola fractional integration and logarithmic integration,Hermite-Hadamard inequality has been refined and generalized.The definition of Katugampola fractional integrals of binary functions is introduced,and a class of Hermite-Hadamard type inequalities is established by using the convexity of univariate function and the coordinated convexity of bivariate function.Hermite-Hadamard inequality,Hermite-Hadamard type fractional integral inequality and Hermite-Hadamard type logarithmic integral inequality of univariate convex functions and bivariate coordinated convex functions are obtained when some special function is considered.

关 键 词：凸函数 协同凸函数 HERMITE-HADAMARD不等式 Katugampola分数阶积分 对数积分 

分 类 号：O172[理学—数学]