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浙江大学学报（理学版）
浙江大学学报（理学版）  2018, Vol. 45 Issue (5): 549-554,561    DOI: 10.3785/j.issn.1008-9497.2018.05.006
数学与计算机科学     
η凸函数的Riemann-Liouville分数阶积分的Hermite-Hadamard型不等式
时统业1, 曾志红2, 曹俊飞3
1. 海军指挥学院, 江苏 南京 211800;
2. 广东第二师范学院 学报编辑部, 广东 广州 510303;
3. 广东第二师范学院 数学系, 广东 广州 510303
Hermite-Hadamard type inequalities involving Riemann-Liouville fractional integrals for η-convex functions
SHI Tongye1, ZENG Zhihong2, CAO Junfei3
1. PLA Naval Command College, Nanjing 211800, China;
2. Editorial Department of Journal, Guangdong University of Education, Guangzhou 510303, China;
3. Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China
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摘要： 对已有的2个η凸函数的分数阶积分的Hermite-Hadamard型不等式进行了改进.在一阶导函数的绝对值为η凸函数的情况下，利用涉及一阶导函数的分数阶积分恒等式，得到了新的分数阶积分的Hermite-Hadamard型不等式.
关键词： η  凸函数;  Hermite-Hadamard型不等式;  分数阶积分    
Abstract: Two existing Hermite-Hadamard type inequalities involving fractional integrals for η-convex functions are improved. By using the fractional integral identities embedding the first order derivative function, new Hermite-Hadamard type inequalities involving fractional integrals are obtained provided that the absolute value of the first derivative function is η-convex function.
Key words: η-convex function    Hermite-Hadamard type inequality    fractional integral
收稿日期: 2018-01-04 出版日期: 2018-09-12
CLC:  O178  
基金资助: 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）；广东省特色创新项目（自然科学）（2016KTSCX094）；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）.
通讯作者: 曾志红,ORCID:http://orcid.org/0000-0001-9684-1397,E-mail:zhzeng@gdei.edu.cn     E-mail: zhzeng@gdei.edu.cn
作者简介: 时统业(1963-),ORCID:http://orcid.org/0000-0001-6142-8906,男,硕士,副教授,主要从事不等式研究.
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引用本文:

时统业, 曾志红, 曹俊飞. η凸函数的Riemann-Liouville分数阶积分的Hermite-Hadamard型不等式[J]. 浙江大学学报（理学版）, 2018, 45(5): 549-554,561.

SHI Tongye, ZENG Zhihong, CAO Junfei. Hermite-Hadamard type inequalities involving Riemann-Liouville fractional integrals for η-convex functions. Journal of ZheJIang University(Science Edition), 2018, 45(5): 549-554,561.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2018.05.006    或    https://www.zjujournals.com/sci/CN/Y2018/V45/I5/549

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