Generalization of some fractional versions of Hadamard inequalities via exponentially (α, h - m)-convex functions

被引:5
|
作者
Lv, Yu-Pei [1 ]
Farid, Ghulam [2 ]
Yasmeen, Hafsa [2 ]
Nazeer, Waqas [3 ]
Jung, Chahn Yong [4 ]
机构
[1] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China
[2] COMSATS Univ Islamabad, Dept Math, Attock Campus, Attock, Pakistan
[3] Govt Coll Univ Lahore, Dept Math, Lahore, Pakistan
[4] Gyeongsang Natl Univ, Dept Business Adm, Jinju 52828, South Korea
来源
AIMS MATHEMATICS | 2021年 / 6卷 / 08期
基金
加拿大自然科学与工程研究理事会;
关键词
(alpha; h - m)-convex function; exponentionally; Hadamard inequality; Riemann-Liouville fractional integrals; M-CONVEX FUNCTIONS; DIFFERENTIABLE MAPPINGS; REAL NUMBERS;
D O I
10.3934/math.2021521
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper we give Hadamard inequalities for exponentially (alpha, h - m)-convex functions using Riemann-Liouville fractional integrals for strictly increasing function. Results for RiemannLiouville fractional integrals of convex, m-convex, s-convex, (alpha, m)-convex, (s, m)-convex, (h - m) convex, (alpha, h - m)-convex, exponentially convex, exponentially m-convex, exponentially s-convex, exponentially (s, m)-convex, exponentially (h - m)-convex, exponentially (alpha, h - m)-convex functions are particular cases of the results of this paper. The error estimations of these inequalities by using two fractional integral identities are also given.
引用
收藏
页码:8978 / 8999
页数:22
相关论文
共 50 条
  • [1] Fractional Versions of Hadamard-Type Inequalities for Strongly Exponentially (α, h - m)-Convex Functions
    Li, Shasha
    Farid, Ghulam
    Rehman, Atiq Ur
    Yasmeen, Hafsa
    JOURNAL OF MATHEMATICS, 2021, 2021
  • [2] FRACTIONAL VERSIONS OF HADAMARD INEQUALITIES FOR STRONGLY (s, m)-CONVEX FUNCTIONS VIA CAPUTO FRACTIONAL DERIVATIVES
    Farid, Ghulam
    Bibi, Sidra
    Rathour, Laxmi
    Mishra, Lakshmi Narayan
    Mishra, Vishnu Narayan
    KOREAN JOURNAL OF MATHEMATICS, 2023, 31 (01): : 75 - 94
  • [3] Fractional Hadamard and Fejer-Hadamard Inequalities Associated with Exponentially (s, m)-Convex Functions
    Guo, Shuya
    Chu, Yu-Ming
    Farid, Ghulam
    Mehmood, Sajid
    Nazeer, Waqas
    JOURNAL OF FUNCTION SPACES, 2020, 2020
  • [4] k-Fractional Integral Inequalities Of Hadamard Type For Strongly Exponentially (α, h - m)-Convex Functions
    Rathour, Laxmi
    Rehman, Atiq Ur
    Bibi, Sidra
    Farid, Ghulam
    Mishra, Lakshmi Narayan
    Mishra, Vishnu Narayan
    APPLIED MATHEMATICS E-NOTES, 2023, 23 : 393 - 411
  • [5] Hadamard-Type k-Fractional Integral Inequalities for Exponentially (α, h - m)-Convex Functions
    Jung, Chahn Yong
    Farid, Ghulam
    Bibi, Sidra
    Nisar, Kottakkaran Sooppy
    Kang, Shin Min
    JOURNAL OF MATHEMATICS, 2020, 2020
  • [6] Some new Caputo fractional derivative inequalities for exponentially (θ, h - m)-convex functions
    Baloch, Imran Abbas
    Abdeljawad, Thabet
    Bibi, Sidra
    Mukheimer, Aiman
    Farid, Ghulam
    Ul Haq, Absar
    AIMS MATHEMATICS, 2021, 7 (02): : 3006 - 3026
  • [7] FRACTIONAL INEQUALITIES FOR SOME EXPONENTIALLY CONVEX FUNCTIONS
    Mehreen, Naila
    Anwar, Matloob
    HONAM MATHEMATICAL JOURNAL, 2020, 42 (04): : 653 - 665
  • [8] Hadamard Type Inequalities for m-convex and (α, m)-convex Functions via Fractional Integrals
    Ardic, Merve Avci
    Ekinci, Alper
    Akdemir, Ahmet Ocak
    Ozdemir, M. Emin
    6TH INTERNATIONAL EURASIAN CONFERENCE ON MATHEMATICAL SCIENCES AND APPLICATIONS (IECMSA-2017), 2018, 1926
  • [9] FRACTIONAL EXPONENTIALLY m-CONVEX FUNCTIONS AND INEQUALITIES
    Rashid, Saima
    Noor, Muhammad Aslam
    Noor, Khalida Inyat
    INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS, 2019, 17 (03): : 464 - 478
  • [10] k-fractional integral inequalities of Hadamard type for exponentially (s, m)-convex functions
    Rehman, Atiq Ur
    Farid, Ghulam
    Bibi, Sidra
    Jung, Chahn Yong
    Kang, Shin Min
    AIMS MATHEMATICS, 2021, 6 (01): : 882 - 892