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浙江大学学报(理学版)  2017, Vol. 44 Issue (5): 531-537    DOI: 10.3785/j.issn.1008-9497.2017.05.006
数学与计算机科学     
分数次积分下关于s-凸函数的新Hermite-Hadamard型不等式
孙文兵
邵阳学院 理学与信息科学系, 湖南 邵阳 422000
New Hermite-Hadamard-type inequalities for s-convex functions via fractional integrals
SUN Wenbing
Department of Science and Information Science, Shaoyang University, Shaoyang 422000, Hunan Province, China
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摘要: 建立了一个关于Riemann-Liouville分数次积分的恒等式, 利用此恒等式, 得到了一些函数为可微且s-凸映射的关于分数次积分的新Hermite-Hadamard型积分不等式, 并且对于可微的s-凹函数也得到一些新的结果. 文中的新结果推广了部分已有研究的结论.最后给出了一个应用实例.
关键词: Hadamard不等式s-凸函数Höder不等式Riemann-Liouville分数次积分    
Abstract: In this paper, we establish a new identity for Riemann-Liouville fractional integrals. Using the established identity, some new Hermite-Hadamard type inequalities for differentiable s-convex mappings that are connected with the Riemann-Liouville fractional integrals are obtained. Also, some results are deduced for differentiable s-concave functions. Our results extend some proved results in the existing researches. Finally, we give an example to illustrate the applications of the results.
Key words: Hadamard's inequality    s-convex function    Hölder inequality    Riemann-Liouville fractional integral
收稿日期: 2016-08-30 出版日期: 2017-05-01
CLC:  O178  
基金资助: 湖南省自然科学基金资助项目(12JJ3008);湖南省教育厅重点项目(14A132);邵阳市科技计划项目(2016GX04).
作者简介: 孙文兵(1978-),ORCID:http://orcid.org/0000-0002-5673-4519,男,硕士,副教授,主要从事解析不等式研究,E-mail:swb0520@163.com.
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孙文兵

引用本文:

孙文兵. 分数次积分下关于s-凸函数的新Hermite-Hadamard型不等式[J]. 浙江大学学报(理学版), 2017, 44(5): 531-537.

SUN Wenbing. New Hermite-Hadamard-type inequalities for s-convex functions via fractional integrals. Journal of ZheJIang University(Science Edition), 2017, 44(5): 531-537.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2017.05.006        https://www.zjujournals.com/sci/CN/Y2017/V44/I5/531

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