Some parameterized Simpson-, midpoint-and trapezoid-type inequalities for generalized fractional integrals

被引:11
作者
Budak, Huseyin [1 ]
Yildirim, Seda Kilinc [2 ]
Sarikaya, Mehmet Zeki [1 ]
Yildirim, Huseyin [2 ]
机构
[1] Duzce Univ, Dept Math, Duzce, Turkey
[2] Univ Kahramanmaras, Fac Sci & Arts, Dept Math, TR-46000 Kahramanmaras, Turkey
关键词
Simpson's 1/3 formula; Integral inequalities; Fractional calculus; Convex functions; HERMITE-HADAMARD-TYPE; DIFFERENTIABLE MAPPINGS; CONVEX FUNCTIONS; REAL NUMBERS;
D O I
10.1186/s13660-022-02773-5
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we first obtain an identity for differentiable mappings. Then, we establish some new generalized inequalities for differentiable convex functions involving some parameters and generalized fractional integrals. We show that these results reduce to several new Simpson-, midpoint- and trapezoid-type inequalities. The results given in this study are the generalizations of results proved in several earlier papers.
引用
收藏
页数:23
相关论文
共 35 条
[1]   Some new Simpson-type inequalities for generalizedp-convex function on fractal sets with applications [J].
Abdeljawad, Thabet ;
Rashid, Saima ;
Hammouch, Zakia ;
Iscan, Imdat ;
Chu, Yu-Ming .
ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
[2]   New quantum boundaries for quantum Simpson's and quantum Newton's type inequalities for preinvex functions [J].
Ali, Muhammad Aamir ;
Abbas, Mujahid ;
Budak, Huseyin ;
Agarwal, Praveen ;
Murtaza, Ghulam ;
Chu, Yu-Ming .
ADVANCES IN DIFFERENCE EQUATIONS, 2021, 2021 (01)
[3]   Some new Simpson's type inequalities for coordinated convex functions in quantum calculus [J].
Ali, Muhammad Aamir ;
Budak, Huseyin ;
Zhang, Zhiyue ;
Yildirim, Huseyin .
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (06) :4515-4540
[4]  
Alomari M., 2009, RES REP, V12, P4
[5]   New midpoint type inequalities for generalized fractional integral [J].
Budak, Huseyin ;
Kara, Hasan ;
Kapucu, Rabia .
COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 2022, 10 (01) :93-108
[6]   On New Extensions of Hermite-Hadamard Inequalities for Generalized Fractional Integrals [J].
Budak, Huseyin ;
Pehlivan, Ebru ;
Kosem, Pinar .
SAHAND COMMUNICATIONS IN MATHEMATICAL ANALYSIS, 2021, 18 (01) :73-88
[7]   Simpson and Newton type inequalities for convex functions via newly defined quantum integrals [J].
Budak, Huseyin ;
Erden, Samet ;
Ali, Muhammad Aamir .
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (01) :378-390
[8]   Some New Inequalities of Simpson's Type for s-convex Functions via Fractional Integrals [J].
Chen, Jianhua ;
Huang, Xianjiu .
FILOMAT, 2017, 31 (15) :4989-4997
[9]   Bounds for the Remainder in Simpson's Inequality vian-Polynomial Convex Functions of Higher Order Using Katugampola Fractional Integrals [J].
Chu, Yu-Ming ;
Awan, Muhammad Uzair ;
Javad, Muhammad Zakria ;
Khan, Awais Gul .
JOURNAL OF MATHEMATICS, 2020, 2020
[10]   Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula [J].
Dragomir, SS ;
Agarwal, RP .
APPLIED MATHEMATICS LETTERS, 1998, 11 (05) :91-95