预不变凸函数的Hermite-Hadamard型分数阶积分不等式的推广

孙文兵; 郑灵红

doi:10.13471/j.cnki.acta.snus.2019.07.02.2019A055

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预不变凸函数的Hermite-Hadamard型分数阶积分不等式的推广

研究论文 | 更新时间：2023-11-01

- 预不变凸函数的Hermite-Hadamard型分数阶积分不等式的推广
- The generalization of Hermite-Hadamard type fractional integrals inequalities for preinvex functions
- 中山大学学报(自然科学版) 2020年59卷第4期页码：149-157
- 作者机构：
  
  邵阳学院理学院,湖南邵阳 422000
- 作者简介：
  
  孙文兵(1978年生），男;研究方向：积分不等式;E-mail：swb0520@163.com
- 基金信息：
  
  湖南省教育厅优秀青年基金(18B433);湖南省自然科学基金(2020JJ5445);国家自然科学基金(61672356)
- DOI：10.13471/j.cnki.acta.snus.2019.07.02.2019A055
  中图分类号： O178
- 纸质出版日期：2020-07-20，
  
  收稿日期：2019-07-03，
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孙文兵,郑灵红.预不变凸函数的Hermite-Hadamard型分数阶积分不等式的推广[J].中山大学学报(自然科学版),2020,59(04):149-157.

SUN Wenbing,ZHENG Linghong.The generalization of Hermite-Hadamard type fractional integrals inequalities for preinvex functions[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2020,59(04):149-157.
孙文兵,郑灵红.预不变凸函数的Hermite-Hadamard型分数阶积分不等式的推广[J].中山大学学报(自然科学版),2020,59(04):149-157. DOI： 10.13471/j.cnki.acta.snus.2019.07.02.2019A055.

SUN Wenbing,ZHENG Linghong.The generalization of Hermite-Hadamard type fractional integrals inequalities for preinvex functions[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2020,59(04):149-157. DOI： 10.13471/j.cnki.acta.snus.2019.07.02.2019A055.

摘要

不变凸子集上构造了一个含参数的关于Riemann-Liouville分数阶积分的恒等式

利用构造的积分恒等式为辅助函数，得到几个函数导数绝对值为预不变凸的新Hermite-Hadamard 型分数阶积分不等式。参数取特定值时得到一些不同形式的积分不等式。

Abstract

An identity with parameter is constructed via Riemann-Liouville fractional integrals on the invex subset.Using the constructed integral identity as the auxiliary function

some new Hermite-Hadamard type fractional integrals inequalities are derived

whose absolute values of the derivatives of the functions are preinvex.When the parameters are taken some specific values

some integral inequalities with different forms are obtained.

关键词

预不变凸函数Hermite-Hadamard型不等式Riemann-Liouville分数阶积分参数推广

Keywords

preinvex functionsHermite-Hadamard type inequalitiesRiemann-Liouville fractional integralsparametergeneralization

references

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孙文兵.分数次积分下关于s-凸函数的新Hermite-Hadamard型不等式[J].浙江大学学报(理学版),2017,44(5):531-537.

SUN W B. New Hermite-Hadamard-type inequalities for s-convex functions via fractional integrals [J]．Journal of Zhejiang University (Science Edition),2017,44(5): 531-537.

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