Hermite-Jensen-Mercer type inequalities via Ψ-Riemann-Liouville k-fractional integrals

被引：13

作者：

Butt, Saad Ihsan ^{[1
]}

Kashuri, Artion ^{[2
]}

Umar, Muhammad ^{[1
]}

Aslam, Adnan ^{[3
]}

Gao, Wei ^{[4
]}

机构：

[1] COMSATS Univ Islamabad, Dept Math, Lahore Campus, Lahore 54000, Pakistan

[2] Univ Ismail Qemali, Fac Tech Sci, Dept Math, Vlora, Albania

[3] Univ Engn & Technol, Dept Nat Sci & Humanities, Lahore RCET, Lahore 54000, Pakistan

[4] Yunnan Normal Univ, Sch Informat Sci & Technol, Kunming 650500, Yunnan, Peoples R China

来源：

AIMS MATHEMATICS | 2020年 / 5卷 / 05期

关键词：

convex function; Hermite-Hadamard inequality; Jensen inequality; Jensen-Mercer inequality; Holder inequality; improved power mean integral inequality; psi-Riemann-Liouville k-Fractional integrals;

D O I：

10.3934/math.2020334

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Integral inequalities involving various fractional integral operators are used to solve many fractional differential equations. In this paper, authors prove some Hermite-Jensen-Mercer type inequalities using Psi-Riemann-Liouville k-Fractional integrals via convex functions. We established some new Psi-Riemann-Liouville k-Fractional integral inequalities. We also give Psi-Riemann-Liouville k-Fractional integrals identities for differentiable mapping, and these will be used to derive estimates for some fractional Hermite-Jensen-Mercer type inequalities. Some known results are recaptured from our results as special cases.

引用

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页码：5193 / 5220

页数：28

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