| 分形集上广义凸函数的新Hermite-Hadamard型不等式及其应用 |
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| 引用本文： | 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. |
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| 作者姓名： | 孙文兵 刘琼 |
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| 作者单位： | 邵阳学院 理学与信息科学系, 湖南 邵阳 422000 |
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| 基金项目： | 邵阳市科技计划项目（2015NC43）；湖南省自然科学基金资助项目（12JJ3008） |
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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(0α≤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.
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| 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 |
| 收稿时间： | 2016-03-22 |
New inequalities of Hermite-Hadamard type for generalized convex functions on fractal sets and its applications |
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| SUN Wenbing,LIU Qiong.New inequalities of Hermite-Hadamard type for generalized convex functions on fractal sets and its applications[J].Journal of Zhejiang University(Sciences Edition),2017,44(1):47-52. |
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| Authors: | SUN Wenbing LIU Qiong |
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| Institution: | Department of Science and Information Science, Shaoyang University, Shaoyang 422000, Hunan Province, China |
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| 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. |
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| Keywords: | Hadamard-type inequalities generalized convex function local fractional integral local fractional derivative fractal space |
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