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《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (4): 81-89.doi: 10.6040/j.issn.1671-9352.0.2022.622

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Ostrowski型分数阶积分不等式的推广

党筱楠(),连铁艳*(),李然   

  1. 陕西科技大学数学与数据科学学院，陕西 西安 710021
  • 收稿日期:2022-11-28 出版日期:2024-04-20 发布日期:2024-04-12
  • 通讯作者: 连铁艳 E-mail:1067641420@qq.com;liantieyan@sust.edu.cn
  • 作者简介:党筱楠(1996—)，女，硕士研究生，研究方向为模糊积分及其应用. E-mail: 1067641420@qq.com
  • 基金资助:
    国家自然科学基金资助项目(11801342);陕西省自然科学基础研究计划资助项目(2023JCYB043)

Some generalizations of Ostrowski type fractional integral inequalities

Xiaonan DANG(),Tieyan LIAN*(),Ran LI   

  1. School of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi'an 710021, Shaanxi, China
  • Received:2022-11-28 Online:2024-04-20 Published:2024-04-12
  • Contact: Tieyan LIAN E-mail:1067641420@qq.com;liantieyan@sust.edu.cn

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摘要：

利用k-β-凸函数与预不变凸函数的定义，提出强k-β-预不变凸函数的定义。通过构建一个k-Riemann-Liouville分数阶积分恒等式，利用强k-β-预不变凸函数的性质及一些积分不等式的方法，建立了一些关于强k-β-预不变凸函数的Ostrowski型k-Riemann-Liouville分数阶积分不等式。

关键词: Ostrowski型不等式, 强k-β-预不变凸函数, k-Riemann-Liouville分数阶积分, Hölder不等式, 幂平均值不等式

Abstract:

By using the definitions of k-β-convex functions and preinvex functions, the definition of strong k-β-preinvex functions is proposed. Based on constructing a k-Riemann-Liouville fractional integral identity, the properties of strong k-β-preinvex functions and some methods of integral inequalities, some Ostrowski type inequalities for strong k-β-preinvex functions via k-Riemann-Liouville fractional integral are established.

Key words: Ostrowski type inequality, strong k-β-preinvex function, k-Riemann-Liouville fractional integral, Hölder inequality, power mean inequality

中图分类号: 

  • O178
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