分形空间上的新Hadamard型不等式及应用

doi:10.3969/j.issn.1000-5641.2017.06.003

华东师范大学学报(自然科学版) ›› 2017, Vol. 2017 ›› Issue (6): 33-41.doi: 10.3969/j.issn.1000-5641.2017.06.003

分形空间上的新Hadamard型不等式及应用

孙文兵

邵阳学院理学院, 湖南邵阳 422000

收稿日期:2016-11-17 出版日期:2017-11-25 发布日期:2017-11-25
作者简介: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.
基金资助:
国家自然科学基金（61672356）；邵阳市科技计划项目（2016GX04）

New Hadamard-type inequalities on fractal space and their applications

SUN Wen-bing

College of Science, Shaoyang University, Shaoyang Hunan 422000, China

Received:2016-11-17 Online:2017-11-25 Published:2017-11-25

摘要/Abstract

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R^α（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

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 R^α(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

中图分类号:

O178

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.

SUN Wen-bing. New Hadamard-type inequalities on fractal space and their applications[J]. Journal of East China Normal University(Natural Sc, 2017, 2017(6): 33-41.

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分形空间上的新Hadamard型不等式及应用

New Hadamard-type inequalities on fractal space and their applications

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