Hermite-Hadamard-type inequalities for Riemann-Liouville fractional integrals via two kinds of convexity

被引：96
|
作者：
Wang, JinRong [1 ]
Li, Xuezhu [1 ]
Feckan, Michal [2 ]
Zhou, Yong [3 ]
机构：
[1] Guizhou Univ, Dept Math, Guiyang 550025, Guizhou, Peoples R China
[2] Comenius Univ, Dept Math Anal & Numer Math, Fac Math Phys & Informat, Bratislava 84248, Slovakia
[3] Xiangtan Univ, Dept Math, Xiangtan 411105, Hunan, Peoples R China
来源：
APPLICABLE ANALYSIS | 2013年 / 92卷 / 11期
关键词：
m-convex functions; (s; m)-convex functions; Hermite-Hadamard-type inequalities; Riemann-Liouville fractional integrals; 26A33; 26A51; 26D15; (ALPHA;
D O I：
10.1080/00036811.2012.727986
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, two fundamental integral identities including the second-order derivatives of a given function via Riemann-Liouville fractional integrals are established. With the help of these two fractional-type integral identities, all kinds of Hermite-Hadamard-type inequalities involving left-sided and right-sided Riemann-Liouville fractional integrals for m-convex and (s,m)-convex functions, respectively. Our methods considered here may be a stimulant for further investigations concerning Hermite-Hadamard-type inequalities involving Hadamard fractional integrals.
引用
收藏
页码：2241 / 2253
页数：13
相关论文
共 50 条
  • [41] Further Hermite-Hadamard-Type Inequalities for Fractional Integrals with Exponential Kernels
    Li, Hong
    Meftah, Badreddine
    Saleh, Wedad
    Xu, Hongyan
    Kilicman, Adem
    Lakhdari, Abdelghani
    FRACTAL AND FRACTIONAL, 2024, 8 (06)
  • [42] On the Hermite–Hadamard type inequality for ψ-Riemann–Liouville fractional integrals via convex functions
    Kui Liu
    JinRong Wang
    Donal O’Regan
    Journal of Inequalities and Applications, 2019
  • [43] Hermite-Hadamard-type inequalities for conformable integrals
    Bohner, Martin
    Kashuri, Artion
    Mohammed, Pshtiwan Othman
    Napoles Valdes, Juan E.
    HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2022, 51 (03): : 775 - 786
  • [44] Hermite-Hadamard-Mercer type inclusions for interval-valued functions via Riemann-Liouville fractional integrals
    Kara, Hasan
    Ali, Muhammad Aamir
    Budak, Huseyin
    TURKISH JOURNAL OF MATHEMATICS, 2022, 46 (06) : 2193 - 2207
  • [45] WEIGHT INEQUALITIES OF THE HARDY TYPE FOR FRACTIONAL RIEMANN-LIOUVILLE INTEGRALS
    STEPANOV, VD
    SIBERIAN MATHEMATICAL JOURNAL, 1990, 31 (03) : 513 - 522
  • [46] On the Hermite-Hadamard-type inequalities for co-ordinated convex function via fractional integrals
    Sarikaya, Mehmet Zeki
    INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2014, 25 (02) : 134 - 147
  • [47] Hermite–Hadamard-type inequalities involving ψ-Riemann–Liouville fractional integrals via s-convex functions
    Yong Zhao
    Haiwei Sang
    Weicheng Xiong
    Zhongwei Cui
    Journal of Inequalities and Applications, 2020
  • [48] Hermite–Hadamard-type inequalities for interval-valued preinvex functions via Riemann–Liouville fractional integrals
    Nidhi Sharma
    Sanjeev Kumar Singh
    Shashi Kant Mishra
    Abdelouahed Hamdi
    Journal of Inequalities and Applications, 2021
  • [49] On new versions of Hermite-Hadamard-type inequalities based on tempered fractional integrals
    Budak, H.
    Hezenci, F.
    Tunc, T.
    Kara, H.
    FILOMAT, 2024, 38 (07) : 2361 - 2379
  • [50] Hermite-Hadamard Inequalities Involving Riemann-Liouville Fractional Integrals via s-convex Functions and Applications to Special Means
    Wang, JinRong
    Li, Xuezhu
    Zhou, Yong
    FILOMAT, 2016, 30 (05) : 1143 - 1150
12345