FRACTIONAL HERMITE-HADAMARD INEQUALITY, SIMPSON'S AND OSTROWSKI'S TYPE INEQUALITIES FOR CONVEX FUNCTIONS WITH RESPECT TO A PAIR OF FUNCTIONS

被引：0

作者：

Xie, Jianqiang ^{[1
]}

Ali, Muhammad Aamir ^{[2
]}

Budak, Huseyin ^{[3
]}

Feckan, Michal ^{[4
,5
]}

Sitthiwirattham, Thanin ^{[6
]}

机构：

[1] Anhui Univ, Sch Math Sci, Hefei, Peoples R China

[2] Nanjing Normal Univ, Sch Math Sci, Nanjing, Peoples R China

[3] Duzce Univ, Dept Math, Duzce, Turkiye

[4] Comenius Univ, Dept Math Anal & Numer Math, Bratislava, Slovakia

[5] Slovak Acad Sci, Math Inst, Bratislava, Slovakia

[6] Suan Dusit Univ, Dept Math, Bangkok, Thailand

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2023年 / 53卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Hermite-Hadamard inequality; Simpson's inequality; Ostrowski's inequality; fractional calculus; (g; h)-convex functions;

D O I：

10.1216/rmj.2023.53.611

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the convexity with respect to a pair of functions and establish a Hermite-Hadamard type inequality for Riemann-Liouville fractional integrals. Moreover, we derive some new Simpson's and Ostrowski's type inequalities for differentiable convex mapping with respect to a pair of functions. We also show that the newly established inequalities are the extension of some existing inequalities. Finally, we consider some mathematical examples and graphs to show the validity of the newly established inequalities.

引用

页码：611 / 628

页数：18

共 32 条

[11] Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals
Iscan, Imdat
Wu, Shanhe
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2014, 238 : 237 - 244
[12] Weighted Midpoint Hermite-Hadamard-Fejer Type Inequalities in Fractional Calculus for Harmonically Convex Functions
Kalsoom, Humaira
Vivas-Cortez, Miguel
Amer Latif, Muhammad
Ahmad, Hijaz
[J]. FRACTAL AND FRACTIONAL, 2021, 5 (04)
[13] Generalized trapezoidal type integral inequalities and their applications
Kashuri, Artion
Liko, Rozana
[J]. JOURNAL OF ANALYSIS, 2020, 28 (04) : 1023 - 1043
[14] Hermite-Hadamard type inequalities for conformable fractional integrals
Khan, M. Adil
Ali, T.
Dragomir, S. S.
Sarikaya, M. Z.
[J]. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2018, 112 (04) : 1033 - 1048
[15] Hermite-Hadamard type inequalities for fractional integrals via Green's function
Khan, Muhammad Adil
Iqbal, Arshad
Suleman, Muhammad
Chu, Yu-Ming
[J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2018,
[16] Kilbas A. A., 2006, N HOLLAND MATH STUDI, V204, DOI DOI 10.1016/S0304-0208(06)80001-0
[17] Some Simpson's Riemann-Liouville Fractional Integral Inequalities with Applications to Special Functions
Nasir, Jamshed
Qaisar, Shahid
Butt, Saad Ihsan
Khan, Khuram Ali
Mabela, Rostin Matendo
[J]. JOURNAL OF FUNCTION SPACES, 2022, 2022
[18] Peng C, 2017, ITAL J PURE APPL MAT, P345
[19] Inequalities by Means of Generalized Proportional Fractional Integral Operators with Respect to Another Function
Rashid, Saima
Jarad, Fahd
Noor, Muhammad Aslam
Kalsoom, Humaira
Chu, Yu-Ming
[J]. MATHEMATICS, 2019, 7 (12)
[20] A Convexity Concept with Respect to a Pair of Functions
Samet, Bessem
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2022, 43 (05) : 522 - 540

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