华东师范大学学报（自然科学版） >

2017 , Vol. 2017 >Issue 6: 33 - 41

DOI: https://doi.org/10.3969/j.issn.1000-5641.2017.06.003

数学

分形空间上的新Hadamard型不等式及应用

  • 孙文兵
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  • 邵阳学院 理学院, 湖南 邵阳 422000
孙文兵,男,副教授,研究方向为解析不等式、智能算法.E-mail:swb0520@163.com.

收稿日期: 2016-11-17

  网络出版日期: 2017-11-25

基金资助

国家自然科学基金（61672356）；邵阳市科技计划项目（2016GX04）

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New Hadamard-type inequalities on fractal space and their applications

  • SUN Wen-bing
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  • College of Science, Shaoyang University, Shaoyang Hunan 422000, China

Received date: 2016-11-17

  Online published: 2017-11-25

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摘要

根据分形集上局部分数阶积分和第二种意义下广义s-凸函数的理论，建立了几个分形集Rα（0 < α ≤ 1）上涉及局部分数积分的Hermite-Hadamard型不等式.最后，给出了所得不等式在数值积分误差估计中的应用.

关键词： Hermite-Hadamard型不等式; 广义s-凸函数; 局部分数积分; 局部分数阶导数; 分形空间

本文引用格式

孙文兵 . 分形空间上的新Hadamard型不等式及应用[J]. 华东师范大学学报（自然科学版）, 2017 , 2017(6) : 33 -41 . DOI: 10.3969/j.issn.1000-5641.2017.06.003

Abstract

In the paper, using local fractional calculus theory and the theory of generalized s-convex function in the second sense on fractal sets, some new Hermite-Hadamard type inequalities involving local fractional integrals on fractal sets Rα(0 < α ≤ 1) were established. Finally, some applications of these inequalities to some error estimates for numerical integration were given.

Key words： Hermite-Hadamard type inequalities; generalized s-convex function; local fractional integral; local fractional derivative; fractal space

参考文献

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