分形空间上广义凸函数的新Simpson型不等式及应用

数学物理学报 ›› 2018, Vol. 38 ›› Issue (6): 1058-1066.

分形空间上广义凸函数的新Simpson型不等式及应用

孙文兵(),刘琼

邵阳学院理学院湖南邵阳 422000

收稿日期:2017-10-31 出版日期:2018-12-26 发布日期:2018-12-27
作者简介:孙文兵, E-mail:swb0520@163.com
基金资助:
国家自然科学基金(61672356);邵阳市科技计划项目(2017GX09)

New Simpson Type Inequalities for Generalized Convex Functions on Fractal Space and Its Applications

Wenbing Sun(),Qiong Liu

School of Science, Shaoyang University, Hunan Shaoyang 422000

Received:2017-10-31 Online:2018-12-26 Published:2018-12-27
Supported by:
Supported by the NSFC(61672356);the Science and Technology Plan Project of Shaoyang City(2017GX09)

摘要/Abstract

摘要：

根据局部分数阶微积分理论以及分形实线的α（0 < α≤1）型集合\begin{document}$\mathbb{R}$\end{document}^α上广义凸函数的定义，获得了几个涉及局部分数阶积分的Simpson型不等式.最后，给出了所得不等式在特殊均值和数值积分中的几个应用.

关键词: Simpson型不等式, 广义凸函数, 局部分数阶导数, 局部分数阶积分

Abstract:

In the paper, the authors use local fractional calculus theory and the definition of generalized convex function on the α type set of the real line numbers \begin{document}$\mathbb{R}$\end{document}^α, some new Simpson-type inequalities involving local fractional integrals are established. Finally, some applications of our obtained inequalities to special means and numerical integration are given.

Key words: Simpson-type inequalities, Generalized convex function, Local fractional derivative, Local fractional integral

中图分类号:

O178

孙文兵,刘琼. 分形空间上广义凸函数的新Simpson型不等式及应用[J]. 数学物理学报, 2018, 38(6): 1058-1066.

Wenbing Sun,Qiong Liu. New Simpson Type Inequalities for Generalized Convex Functions on Fractal Space and Its Applications[J]. Acta mathematica scientia,Series A, 2018, 38(6): 1058-1066.

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