引用本文:曾志红, 时统业, 曹俊飞.AR凸函数的Hermite-Hadamard型不等式[J].西南大学学报(自然科学版),2019,41(4):97~103
【打印本页】   【HTML】   【下载PDF全文】   查看/发表评论  【EndNote】   【RefMan】   【BibTex】
←前一篇|后一篇→ 过刊浏览    高级检索
本文已被:浏览 180次   下载 160 本文二维码信息
码上扫一扫!
分享到: 微信 更多
AR凸函数的Hermite-Hadamard型不等式
曾志红, 时统业, 曹俊飞1,2,3
1. 广东第二师范学院 学报编辑部, 广州 510303;2. 海军指挥学院, 南京 211800;3. 广东第二师范学院 数学系, 广州 510303
摘要:
建立AR凸函数的积分不等式,特别是Hermite-Hadamard型不等式.利用通常凸函数与AR凸函数的关系,证明了AR凸函数的单侧导数的存在性和单调性,并通过不等式建立了AR凸函数与其单侧导数的关系.从AR凸函数的定义出发,得到了AR凸函数的Hermite-Hadamard型不等式.利用AR凸函数与其单侧导数的关系,使用数学分析的方法,研究了由AR凸函数的Hermite-Hadamard型不等式生成的差值.利用AR凸函数与其单侧导数的关系,构造了与AR凸函数有关的单调函数,从而给出AR凸函数的定积分的上界和下界.另外,利用AR凸函数与其单侧导数的关系,还建立了AR凸函数的其他的积分不等式.
关键词:  AR凸函数  Hermite-Hadamard型不等式  积分不等式
DOI:10.13718/j.cnki.xdzk.2019.04.014
分类号:O174.13;O178
基金项目:国家自然科学基金青年科学基金项目(11301090);广东省自然科学基金自由申请项目(2015A030313896);广州市科学(技术)研究专项一般项目(201707010230);广东第二师范学院教授博士专项科研经费资助项目(2015ARF24).
Hermite-Hadamard Type Inequalities for AR-Convex Functions
ZENG Zhi-hong, SHI Tong-ye, CAO Jun-fei1,2,3
1. Editorial Department of Journal, Guangdong University of Education, Guangzhou 510303, China;2. PLA Naval Command College, Nanjing 211800, China;3. Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China
Abstract:
The integral inequalities of AR-convex functions, especially the Hermite-Hadamard inequalities, are established. With the aid of the relationship between convex functions and AR-convex functions, the existence and monotonicity of unilateral derivatives of AR-convex functions are proved, and the relationship between AR-convex functions and their unilateral derivatives is established through inequalities. Starting from the definition of AR-convex functions, the Hermite-Hadamard type inequalities for AR-convex functions are obtained. By using the relationship between AR-convex functions and their unilateral derivatives or using mathematical analysis, the difference generated by the Hermite-Hadamard type inequality of AR-convex functions is studied. By using the relationship between AR-convex functions and their unilateral derivatives, the monotone function related to AR-convex functions is constructed, and the upper and lower bounds of the definite integral of AR-convex function are given. In addition, by using the relationship between AR-convex functions and their unilateral derivatives, other integral inequalities of AR-convex functions are established.
Key words:  AR-convex function  Hermite-Hadamard type inequality  integral inequality
手机扫一扫看