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浙江大学学报（理学版）
浙江大学学报（理学版）  2017, Vol. 44 Issue (1): 47-52    DOI: 10.3785/j.issn.1008-9497.2017.01.007
数学与计算机科学     
分形集上广义凸函数的新Hermite-Hadamard型不等式及其应用
孙文兵, 刘琼
邵阳学院 理学与信息科学系, 湖南 邵阳 422000
New inequalities of Hermite-Hadamard type for generalized convex functions on fractal sets and its applications
SUN Wenbing, LIU Qiong
Department of Science and Information Science, Shaoyang University, Shaoyang 422000, Hunan Province, China
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摘要： 基于局部分数阶微积分理论,利用分形集上广义凸函数的定义，对Hermite-Hadamard型不等式进行一些有意义的推广,得到了几个分形集Rα（0<α≤1）上涉及局部分数积分的新Hadamard型不等式.最后,给出了其在特殊均值和数值积分中的几个应用.
关键词： Hadamard型不等式;  广义凸函数;  局部分数积分;  局部分数阶导数;  分形空间    
Abstract: On the basis of local fractional calculus theory, inequalities of Hermite-Hadamard type are extended following the definition of generalized convex function on fractal sets. Some new Hadamard-type inequalities involving local fractional integrals on fractal sets Rα(0<α ≤ 1) are established. Finally, some applications of the new inequalities in special means and numerical integration are provided.
Key words: Hadamard-type inequalities    generalized convex function    local fractional integral    local fractional derivative    fractal space
收稿日期: 2016-03-22 出版日期: 2017-01-22
CLC:  O178  
基金资助: 邵阳市科技计划项目（2015NC43）；湖南省自然科学基金资助项目（12JJ3008）
作者简介: 孙文兵(1978-),ORCID:http://orcid.org/0000-0002-5673-4519,男,硕士,讲师,主要从事解析不等式、智能算法研究,E-mail:swb0520@163.com.
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孙文兵, 刘琼. 分形集上广义凸函数的新Hermite-Hadamard型不等式及其应用[J]. 浙江大学学报（理学版）, 2017, 44(1): 47-52.

SUN Wenbing, LIU Qiong. New inequalities of Hermite-Hadamard type for generalized convex functions on fractal sets and its applications. Journal of ZheJIang University(Science Edition), 2017, 44(1): 47-52.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2017.01.007    或    https://www.zjujournals.com/sci/CN/Y2017/V44/I1/47

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