A Note on Fractional Simpson Type Inequalities for Twice Differentiable Functions

被引：5

作者：

Hezenci, Fatih ^{[1
]}

机构：

[1] Duzce Univ, Dept Math, Fac Sci & Arts, Duzce, Turkiye

来源：

MATHEMATICA SLOVACA | 2023年 / 73卷 / 03期

关键词：

Simpson type inequalities; convex function; fractional integrals; twice differentiable function; INTEGRAL-INEQUALITIES; CONVEX-FUNCTIONS;

D O I：

10.1515/ms-2023-0049

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, an equality is proved for twice differentiable convex functions involving Riemann-Liouville fractional integral. With the help of this equality, there are established several fractional Simpson type inequalities for functions whose second derivatives in absolute value are convex. By using special cases of the main results, previously obtained Simpson type inequalities are found for the Riemann-Liouville fractional integral.

引用

页码：675 / 686

页数：12

共 37 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] Some generalized Riemann-Liouville k-fractional integral inequalities [J].

Agarwal, Praveen ;

Tariboon, Jessada ;

Ntouyas, Sotiris K. .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016,

[3] Some New Simpson's-Formula-Type Inequalities for Twice-Differentiable Convex Functions via Generalized Fractional Operators [J].

Ali, Muhammad Aamir ;

Kara, Hasan ;

Tariboon, Jessada ;

Asawasamrit, Suphawat ;

Budak, Huseyin ;

Hezenci, Fatih .

SYMMETRY-BASEL, 2021, 13 (12)

[4]

Alomari M., 2009, RGMIA RES REP COLL, V12, P9

[5] On generalized Ostrowski, Simpson and Trapezoidal type inequalities for co-ordinated convex functions via generalized fractional integrals [J].

Budak, Huseyin ;

Hezenci, Fatih ;

Kara, Hasan .

ADVANCES IN DIFFERENCE EQUATIONS, 2021, 2021 (01)

[6] On parameterized inequalities of Ostrowski and Simpson type for convex functions via generalized fractional integrals [J].

Budak, Huseyin ;

Hezenci, Fatih ;

Kara, Hasan .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (17) :12522-12536

[7] 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

[8] On Simpson's inequality and applications [J].

Dragomir, SS ;

Agarwal, RP ;

Cerone, P .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2000, 5 (06) :533-579

[9] A generalization of Simpson's inequality via differentiable mapping using extended (s, m)-convex functions [J].

Du, Tingsong ;

Li, Yujiao ;

Yang, Zhiqiao .

APPLIED MATHEMATICS AND COMPUTATION, 2017, 293 :358-369

[10] Simpson type integral inequalities for generalized fractional integral [J].

Ertugral, Fatma ;

Sarikaya, Mehmet Zeki .

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2019, 113 (04) :3115-3124

← 1 2 3 4 →