内蒙古民族大学学报（自然科学版）2025，Vol.40Issue(1)：7-16,10.DOI:10.14045/j.cnki.15-1220.2025.01.002
Hermite-Hadamard不等式的一类推广
A Kind of Generalization for Hermite-Hadamard Inequality
摘要
Abstract
Based on Katugampola fractional integration and logarithmic integration,Hermite-Hadamard inequali-ty has been refined and generalized.The definition of Katugampola fractional integrals of binary functions is intro-duced,and a class of Hermite-Hadamard type inequalities is established by using the convexity of univariate func-tion 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 func-tions 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Key words
convex function/coordinated convex function/Hermite-Hadamard inequality/Katugampola fraction-al integral/logarithmic integral分类
数理科学引用本文复制引用
包琳娜,王淑红..Hermite-Hadamard不等式的一类推广[J].内蒙古民族大学学报（自然科学版）,2025,40(1):7-16,10.基金项目
国家自然科学基金项目(12361013) （12361013）
内蒙古自治区直属高校基本科研业务费项目(GXKY22159) （GXKY22159）
