<em>η</em>凸函数的Riemann-Liouville分数阶积分的Hermite-Hadamard型不等式

doi:10.3785/j.issn.1008-9497.2018.05.006

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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.

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	时统业
	曾志红
	曹俊飞

关键词 ： &eta, 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

ZTFLH:

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.

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.

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

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