中山大学学报(自然科学版) ›› 2020, Vol. 59 ›› Issue (4): 149-157.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

孙文兵, 郑灵红   

  1. 邵阳学院理学院,湖南 邵阳 422000
  • 收稿日期:2019-07-03 出版日期:2020-07-25 发布日期:2020-07-25

The generalization of Hermite-Hadamard type fractional integrals inequalities for preinvex functions

SUN Wenbing, ZHENG Linghong   

  1. School of ScienceShaoyang UniversityShaoyang 422000China
  • Received:2019-07-03 Online:2020-07-25 Published:2020-07-25
  • About author:孙文兵(1978年生),男;研究方向:积分不等式;E-mail:swb0520@163.com

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。

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

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.

Key words: preinvex functions,  , Hermite-Hadamard type inequalities,  , Riemann-Liouville fractional integrals,  , parameter,  , generalization

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