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浙江大学学报（理学版）
浙江大学学报（理学版）  2019, Vol. 46 Issue (5): 543-549    DOI: 10.3785/j.issn.1008-9497.2019.05.005
数学与计算机科学     
分形空间中的广义预不变凸函数与相关的Hermite-Hadamard型积分不等式
孙文兵
邵阳学院 理学院, 湖南 邵阳 422000
Generalized preinvex functions and related Hermite-Hadamard type integral inequalities on fractal space.
SUN Wenbing
School of Science, Shaoyang University, Shaoyang 422000, Hunan Province,China
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摘要： 在分形集Rα(0<α≤1)上定义了广义预不变凸函数, 建立了关于广义预不变凸函数的 Hermite-Hadamard积分不等式。 构建了一个与广义预不变凸函数相关的局部分数阶积分恒等式, 由此恒等式并利用广义Hölder不等式和广义幂均不等式得到了关于此类函数的几个Hermite-Hadamard型局部分数阶积分不等式。 结果推广了已有研究中的一些结论。
关键词： 广义预不变凸函数;  Hermite-Hadamard 型不等式;  广义H?lder不等式;  分形集;  局部分数阶积分    
Abstract: This paper proposes the author proposed the concept of generalized preinvex function on fractal sets Rα(0<α≤ 1) and establishes generalizes Hermite-Hadamard’s inequalities for generalized preinvex function. Then, a local fractional integral identity for generalized preinvex function is established. Using this identity, by generalized Hölder inequality and generalized power-mean inequality, some Hermite-Hadamard type inequalities for this type of function via local fractional integral are obtained. These results extend some results of the existing researches.
Key words: generalized preinvex convex function    Hermite-Hadamard type inequality    generalized H?lder inequality    fractal sets    local fractional integral
收稿日期: 2018-10-11 出版日期: 2019-09-25
CLC:  O178  
基金资助: 湖南省教育厅青年项目（18B433）；国家自然科学基金资助项目( 61672356)。
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.
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孙文兵

引用本文:

孙文兵. 分形空间中的广义预不变凸函数与相关的Hermite-Hadamard型积分不等式[J]. 浙江大学学报（理学版）, 2019, 46(5): 543-549.

SUN Wenbing. Generalized preinvex functions and related Hermite-Hadamard type integral inequalities on fractal space.. Journal of ZheJIang University(Science Edition), 2019, 46(5): 543-549.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2019.05.005    或    https://www.zjujournals.com/sci/CN/Y2019/V46/I5/543

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