Fractional Versions of Hadamard-Type Inequalities for Strongly Exponentially (α, h - m)-Convex Functions

被引:0
作者
Li, Shasha [1 ]
Farid, Ghulam [2 ]
Rehman, Atiq Ur [2 ]
Yasmeen, Hafsa [2 ]
机构
[1] Harbin Univ Sci & Technol, Dept Math, Harbin 150000, Heilongjiang, Peoples R China
[2] COMSATS Univ Islamabad, Dept Math, Attock Campus, Attock, Pakistan
关键词
M-CONVEX FUNCTIONS; DIFFERENTIABLE MAPPINGS; INTEGRAL-INEQUALITIES; REAL NUMBERS;
D O I
10.1155/2021/2555974
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this article, we prove some fractional versions of Hadamard-type inequalities for strongly exponentially (alpha, h - m)-convex functions via generalized Riemann-Liouville fractional integrals. The outcomes of this paper provide inequalities of strongly convex, strongly m-convex, strongly s-convex, strongly (alpha, m)-convex, strongly (s, m)-convex, strongly (h - m)-convex, strongly (alpha, h - m)-convex, strongly exponentially convex, strongly exponentially m-convex, strongly exponentially s-convex, strongly exponentially (s, m)-convex, strongly exponentially (h - m)-convex, and exponentially (alpha, h - m)-convex functions. The error estimations are also studied by applying two fractional integral identities.
引用
收藏
页数:23
相关论文
共 50 条
[21]   Hermite-Hadamard type inequalities for the m- and (α, m)-geometrically convex functions [J].
Xi, Bo-Yan ;
Bai, Rui-Fang ;
Qi, Feng .
AEQUATIONES MATHEMATICAE, 2012, 84 (03) :261-269
[22]   Hermite-Hadamard type inequalities for the m- and (α, m)-logarithmically convex functions [J].
Bai, Rui-Fang ;
Qi, Feng ;
Xi, Bo-Yan .
FILOMAT, 2013, 27 (01) :1-7
[23]   On some inequalities related to fractional Hermite-Hadamard type for differentiable convex functions [J].
Budak, Huseyin ;
Kara, Hasan ;
Ali, Muhammad Aamir ;
Kiris, Mehmet Eyup .
ANNALS OF THE UNIVERSITY OF CRAIOVA-MATHEMATICS AND COMPUTER SCIENCE SERIES, 2021, 48 (02) :222-233
[24]   Integral inequalities of Hermite-Hadamard type for (α, s)-convex and (α, s,m)-convex functions [J].
Xi, Bo-Yan ;
Gao, Dan-Dan ;
Qi, Feng .
ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2020, (44) :499-510
[25]   Generalizations of fractional Hermite-Hadamard-Mercer like inequalities for convex functions [J].
Vivas-Cortez, Miguel ;
Ali, Muhammad Aamir ;
Kashuri, Artion ;
Budak, Huseyin .
AIMS MATHEMATICS, 2021, 6 (09) :9397-9421
[26]   Inequalities for Riemann-Liouville Fractional Integrals of Strongly (s, m)-Convex Functions [J].
Zhang, Fuzhen ;
Farid, Ghulam ;
Akbar, Saira Bano .
JOURNAL OF MATHEMATICS, 2021, 2021
[27]   On the Hadamard's type Inequalities for Convex Functions via Conformable Fractional Integrals [J].
Yildirim, M. E. ;
Akkurt, A. ;
Yildirim, H. .
JOURNAL OF INEQUALITIES AND SPECIAL FUNCTIONS, 2018, 9 (03) :1-10
[28]   New Hermite-Hadamard Type Inequalities for Exponentially GA and GG-Convex Functions [J].
Rashid, Saima ;
Noor, Muhammad Aslam ;
Noor, Khalida Inayat ;
Safdar, Farhat .
PUNJAB UNIVERSITY JOURNAL OF MATHEMATICS, 2020, 52 (02) :15-28
[29]   Integral inequalities of Hermite-Hadamard type for (α, m)-GA-convex functions [J].
Ji, Ai-Ping ;
Zhang, Tian-Yu ;
Qi, Feng .
JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2015, 18 (02) :255-265
[30]   Some Hermite-Hadamard Type Inequalities for h-Convex Functions and their Applications [J].
Ogulmus, Hatice ;
Sarikaya, Mehmet Zeki .
IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, 2020, 44 (03) :813-819