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山东大学学报(理学版) ›› 2016, Vol. 51 ›› Issue (8): 22-28.doi: 10.6040/j.issn.1671-9352.0.2015.634

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基于模糊积分的Hermite-Hadamard和Sandaor类型的不等式

卢威,宋晓秋*,黄雷雷   

  1. 中国矿业大学理学院, 江苏 徐州 221116
  • 收稿日期:2015-12-29 出版日期:2016-08-20 发布日期:2016-08-08
  • 通讯作者: 宋晓秋(1963— ),男, 教授, 研究方向为应用泛函分析、模糊数学相关理论与应用研究. E-mail:songxiaoqiu5201@163.com E-mail:luweilukai@163.com
  • 作者简介:卢威(1989—), 男, 硕士研究生, 研究方向为泛函分析、模糊数学相关理论与应用研究. E-mail:luweilukai@163.com
  • 基金资助:
    国家自然科学基金面上资助项目(51374199)

Inequalities of Hermite-Hadamard and Sandaor for fuzzy integral

LU Wei, SONG Xiao-qiu*, HUANG Lei-lei   

  1. College of Science, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China
  • Received:2015-12-29 Online:2016-08-20 Published:2016-08-08

摘要: 通过给出r-凸函数和Orlicz-凸函数函数定义,首先证明了基于r-凸函数的Sandor类型的模糊积分不等式,随后证明了基于Orlicz-凸函数的Hermite-Hadamard类型模糊积分不等式。最后给出一些例子来验证得到的结论。

关键词: Sandaor不等式, Orlicz-凸函数, Hermite-Hadamard不等式, r-凸函数

Abstract: On the basis of the definitions of r-convex function and Orlicz-convex function, Sandors type inequality for fuzzy integrals upon r-convex function is proved. Hermite-Hadamard type inequality for fuzzy integrals based on Orlicz-convex function is investigated. Some examples are given to illustrate our theorems.

Key words: Orlicz-convex function, Sandors type inequality, r-convex function, Hermite-Hadamard type inequality

中图分类号: 

  • O159
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