摘要
利用凸函数与调和凸函数的关系,建立调和凸函数的加权Hermite-Hadamard型不等式,证明调和凸函数单侧导数的存在性和单调性,并通过不等式建立了调和凸函数与其单侧导数的联系,由此获得关于调和凸函数的积分不等式.
On the basis of the relationship between convex functions and harmonically convex functions,a weighted Hermite-Hadamard type inequality for harmonically convex functions is established,the existence and the monotonicity of unilateral derivatives of harmonically convex functions are proved,and the relation between harmonically convex functions and its derivative is established through inequalities.Integral inequalities for harmonically convex functions are obtained.
作者
时统业
曾志红
陈强
SHI Tong-ye;ZENG Zhi-hong;CHEN Qiang(PLA Naval Command College,Nanjing 211800,China;Editorial Department of Journal,Guangdong University of Education,Guangzhou 510303,China;Department of Computer Science,Guangdong University of Education,Guangzhou 510303,China)
出处
《广州大学学报（自然科学版）》
CAS
2018年第5期21-27,共7页
Journal of Guangzhou University:Natural Science Edition
基金
国家自然科学基金资助项目(61772140)
广东省省级科技计划资助项目(2017A010101021)
广东第二师范学院教授博士专项科研经费资助项目(2015ARF24)
关键词
调和凸函数
积分不等式
单侧导数
harmonically convex function
integral inequality
unilateral derivative
